Both players fought hard in a first set full of baseline winners but were forced off by persistent showers, with Stephens serving to stay alive at 5-4.
Bartoli reacted quickest when a delay of more than two hours finally ended, quickly claiming the first set in clinical fashion.
Despite a remarkable run of eight successive breaks from both women it was Bartoli who held her nerve, securing a straight-sets win 6-4 7-5.
Look back at how the 28-year-old booked her third semi-final appearance at SW19 with Sports Mole's minute-by-minute coverage below.
2.33pmAfternoon tennis fans. Thanks for joining Sports Mole as quarter-finals day in the women's singles continues with a clash between Sloane Stephens and Marion Bartoli on Court One.
2.35pmThankfully a passing shower seems to have only resulted in a short delay to this match starting on Court One, with the covers taken off after just 15 minutes. Both players are due in just a moment for what promises to be an intriguing clash between youth and experience.
2.37pmTwenty-year-old Stephens is enjoying a quite remarkable season, which began with a run to the semi-finals of the Australian Open. The American has carried that fine form into the grass court season, reaching the last eight at SW19 after coming through a succession of tight three-set encounters.
2.39pmBartoli has considerable Wimbledon experience in her favour this afternoon, with the Frenchwoman a former finalist in this tournament. With victories over the likes of Justine Henin in previous years at SW19 the world number 15 will be confident of progression today, after winning all four matches in straight sets to reach this stage.
2.41pmBoth players are just about finished with the pre-match rituals on a slightly overcast Court One, with Bartoli to serve first. It will be interesting to see how Stephens copes with the pressure this afternoon, after a particularly gruelling run to her first Wimbledon quarter-final.
2.43pmHere we go then, with Bartoli to serve first. In the very first point Stephens shows superb variety with a drop shot, catching her opponent by surprise to put an early marker down that the youngster means business.
Stephens *0-1 BartoliA strong effort there from Bartoli to get the opening hold, showing power and depth to force errors in successive baseline rallies. That is what the 28-year-old has based her success on at SW19 in recent years, grinding out tough points deep at the back of the court.
Stephens 1-1* BartoliHeavy hitting from Bartoli puts Stephens under pressure in her first service game, slamming a baseline winner across court to reach deuce. A very positive response from the American starlet though, following a forehand winner with a first ace to ease her way into the match.
Stephens *1-2 BartoliA welcome love game for the former finalist, putting nice variety behind a noticeably different service action. Stephens looked happy to stay defensive at the baseline in that game, perhaps just taking her foot of the pedal after making her opening hold.
Stephens 2-2* BartoliMore confident serving sees Stephens crash a second ace down the middle, before a clever wide serve soon makes it ace number three. Bartoli just caught on her heels there deep at the baseline, allowing the American to quickly claim a love service game of her own.
Stephens *2-3 BartoliMake that 11 successive point won on serve, with Bartoli quickly building a 40-0 lead behind a wide backhand winner. An unforced error from the Frenchwoman proves to be just a momentary blip, with a strong first serve helping keep this first set firmly on serve in the early going.
3.00pmBartoli has rather strangely just passed a pair of her rackets over to her coaching team, with the aim of getting her spares re-strung ahead of the second set perhaps. When play resumes a stray forehand goes well wide from Stephens, with a double fault soon following to put the American under pressure at 0-30.
3.02pmBREAK POINTS! An early forehand drive down the line is just too good from Bartoli, earning the world number 15 three break points and a chance to take charge of the first set.
Stephens 3-3* BartoliAggression and quite magnificent hitting get the youngster out of deep trouble on serve. Two wide serves are followed up by a precise volley at the net to force deuce, with Bartoli biting right back to aim a fine forehand pass across court. More gutsy play at the net earns a tough hold for the 20-year-old.
Stephens *3-4 BartoliConfident hitting on the Stephens forehand puts Bartoli under some strain on serve at 30-30, but a precise first serve soon eases the veteran ahead. A slack forehand from the American then allows Bartoli to earn the seventh successive hold of the match.
3.10pmBartoli has never been a conventional player and just stubbornly refuses to sit down during a short break, crouching down as if to stave off cramp before asking the umpire for a tissue. Stephens takes no notice as she focuses on maintaining an encouraging start on serve.
Stephens 4-4* BartoliThe American has wasted no time in finding accuracy with her first serve, earning a second hold to love in the process under little pressure.
3.15pmBREAK POINT! A wasteful error from Bartoli at the net hands her opponent break point at 30-40, with a sloppy backhand volley falling short at the net. A high-quality baseline exchange follows in the next but Bartoli's power does the trick, sending a massive backhand down the line to level her service game at deuce.
Stephens *4-5 BartoliBoth players are really stepping up the intensity now in a series of increasingly gruelling baseline rallies. Stephens shows superb defence at the baseline to force deuce four times but Bartoili holds her never to come through, saving two break-point chances in the process.
3.23pmStephens is consistently getting a wide first serve in play to great effect, but gets caught driving inside too early by a fierce baseline return from Bartoli to go 15-30 behind on serve.
3.24pmSET POINT! And just as I praise the Stephens first serve it all starts to unravel for the young American. A pair of sloppy efforts up the middle are caught early and with pace by Bartoli, earning her two set points.
3.28pmA superb show of speed helps Stephens escape a fifth break point, but a stray forehand in the next point has her back under pressure at deuce. Great length from Bartoli is making this crucial game very close, but worryingly there are spots of rain clearly falling on Court One.
3.30pmBartoli clearly does not want to continue in this drizzly conditions, complaining to the umpire that the baseline is treacherous on her side of the court. Both players are now sitting down to see how this shower develops, but Stephens and the crowd are both unhappy with the Frenchwoman's protests.
3.33pmPLAY SUSPENDED! With the rain getting heavier both players have been instructed to wait off court for a few minutes. The umpire has explained that this should only be a temporary delay, so fingers crossed that the covers come off quickly.
3.36pmWell unfortunately the match has been paused at a crucial point for Stephens, with the American at deuce serving to stay in the first set. Bartoli used all her experience to force that delay a couple of points early there, cranking up the pressure on her younger opponent.
3.39pmOver on Centre Court there has play has also been stopped for this shower, with Agnieszka Radwanska an early break up in the deciding set against Li Na. Both players have fought hard in that match but are now quite frustratingly in the middle of a second break for bad weather.
3.42pmUnfortunately this shower has shown no signs of letting up in the last few minutes, with tournament organisers deciding to close the roof on Centre Court as a result. No such luck for us on Court One, but as soon we have an update on a return to play you will be the first to hear it.
3.46pmWhile we wait for news from tournament officials there is time to tell you about an earlier quarter-final result. New bookies favourite in the women's singles Sabine Lisicki has eased through to the final four with a straight-sets win over Kaia Kanepi.
3.50pmUnfortunately still no sign of the covers coming of on Court One, with a persistent drizzle still lingering. An official Tweet from Wimbledon organisers came just a moment ago though and did sound promising for a quick return to play.
3.53pmThe tweet from Wimbledon's official account read as follows: "Rain shower not expected to last long. Another #Wimbledon weather update coming your way shortly."
4.10pmUnfortunately a full 15 minutes after that update the covers are still very much keeping a tight quarter-final between Sloane Stephens and Marion Bartoli from resuming. Play is back underway on Centre Court though, with live updates available to follow by clicking here.
4.30pmCOVERS COMING OFF! After a delay of just over an hour the covers are finally being deflated on Court One, which means we are around 10 minutes from getting our feature quarter-final match back in play.
4.35pmUtter confusion now on Court One, with the covers going straight back on almost instantly as the rain comes back at a trickle. Looks like my hope for a return to action was raised for nothing. Very disappointing for the crowd but even more frustrating for the two players, who were both just hitting their stride in an entertaining first set before the weather worsened.
4.40pmWhile play remains in limbo on Court One we can bring you news of a winner on centre, with Agnieszka Radwanska edging past Li Na in three tough sets. The fourth seed will take some stopping this year, with a formidable baseline game.
4.50pmThe weather forecast did promise a few showers this afternoon, but not a delay approaching two hours for the outside courts. While our frustrating delay continues you can keep track with the final women's quarter-final between Petra Kvitova and Kirsten Flipkens by clicking here. Hope to be back with more positive news of a return very shortly!
5.40pmCOVERS ARE OFF! Finally we look ready for a return to play on Court One, the rain has stopped and the covers have been deflated and removed. Expect play to resume in around 10 minutes time!
5.43pmAfter a lengthy delay the court needs an inspection from tournament officials before play can resume. Here's a message we have just received from the tournament's official Twitter account: "The covers have now been removed from No.1 & outside courts. As soon as courts are inspected we'll tweet play resumption time."
5.47pmThings are looking good for a return to play on Court One, with the umpire's chair rolled back out into place and the line judges back out and visible. Just for the players now and we should we about ready to resume.
5.50pmA reminder that when we do eventually get this match back in full flow Sloane Stephens is in a precarious position, serving to stay in the first set 4-5. The game is finely poised at deuce, affording both players no time to find their feet after a delay of more than two hours.
5.53pmHere come the players back onto Court One at last, with both players needing a few minutes to warm up and leaving their tracksuits on for now. It will very interesting to see how Stephens deals with such a long delay at just 20 years of age, while Bartoli is well versed in playing the waiting game at SW19.
5.56pmJust about ready to get this quarter-final back underway then, so thankfully we can ignore a gloomy grey sky for at least a short while. Stephens must find form instantly to stay in this first set, with Bartoli just two points away from a timely break.
5.58pmSET POINT! Stephens sends a forehand well past the baseline in her first point back on serve, handing Bartoli her third set point.
Stephens 4-6* BartoliSET! And just like that Bartoli has taken the opening set, in rather fortunate circumstances. A poor choice of drop set caught Stephens by surprise, with the American chasing the ball down easily but still managing to miss the net with a forehand pass.
Stephens 4-6 *0-1 BartoliA hold to love sees Bartoli make her experience count to claim successive game since the resumption, winning six points in a row in the process. Stephens is yet to get going since that rain delay and needs to find a hold desperately in her next service game.
6.06pmBREAK POINTS! The Court One crowd is clearly getting behind the young American, booing Bartoli loudly as they remember her insistence on leaving the court at the first sign of drizzle. Stephens still can't win a point though, drifting two forehands against the net to give her opponent three break points at 0-40.
Stephens 4-6 0-2* BartoliBREAK! All too easy for the experienced Bartoli, who gets the early break in the second set by staying strong with a backhand return down the line. You have to make the former finalist favourite for the match now, with Stephens struggling to deal with adverse conditions this evening.
6.09pmFinally some signs of life from Stephens, beating her opponent with a precise forehand pass across court. The 20-year-old slaps her leg as she looks to build momentum with a 15-30 lead on the Bartoli serve.
Stephens 4-6 *1-2 BartoliBREAK! A superb effort from Stephens and this match is firmly back in the balance. The American took advantage of a pair of double faults from Bartoli, finishing a long baseline exchange at break point by slamming a forehand into the corner. Stephens looks fired up and ready for a fight tonight on Court One, much to the obvious pleasure of a crowd rooting for the 20-year-old.
Stephens 4-6 1-3* BartoliBREAK! Inconsistency is blighting Stephens game as back on serve she quickly falls 0-40 behind. A fourth unforced error quickly follows and Bartoli has her third break in a row, easing ahead by a set and a break in a topsy-turvy quarter-final.
6.17pmBREAK POINTS! A raw exchange of power between the two players sees Stephens fight back once more, easing a strong forehand winner up the line to edge 0-30 ahead. Bartoli looks rattled and quickly sends a forehand of her own short at the net, handing the American three chances for another break.
Stephens 4-6 *2-3 BartoliA quite incredible passage of play continues on Court One as Stephens forces the fourth break of serve in as many games. Bartoli just could not live with her young adversary at the baseline in that game, getting caught each time she was forced to be conservative behind a second serve.
6.22pmBREAK POINTS! Neither player can seem to find a way to settle on serve in the second, with Stephens the latest to fall 0-30 behind as she fails to send a forehand slice past the net. I make that 14 successive points won against serve now, giving Bartoli another three break points rather cheaply.
Stephens 4-6 2-4* BartoliBREAK! Five straight breaks of serve now as Bartoli uses sheer power on her backhand side to reclaim her second-set advantage. A hold now for the Italian could prove decisive as Stephens continues to struggle at the baseline.
6.26pmBREAK POINT! A heavy forehand deep down the line from Stephens keeps an unpredictable second set in the balance at 30-30, with Bartoli caught flat-footed at the baseline in the very next point. Make that another chance to break for the American, one she must surely take too!
Stephens 4-6 *3-4 BartoliBREAK! A sixth successive break of serve means that this second set is now bordering on the ridiculous. A packed Court One is clearly delighted with another superb response from Stephens though, as she uses swift movement to find a forehand winner inside the baseline. Can she finally get a hold in the next service game that would boost her chances considerably?
Stephens 4-6 3-5* BartoliBREAK! Well under pressure you have to say Stephens has buckled there. At 0-40 down she goes too bold on second serve, crashing a double fault well past its intended target. Make that seven successive breaks now, which apart from a confused scoreboard mean that Bartoli will now serve for the match.
6.33pmStephens won't go down with a fight in this game, smashing a superb, measured backhand off the baseline. Bartoli is then caught deep at the baseline to send this potentially decisive game to 30-30.
6.36pmBREAK POINT! What an effort at the net from the American teenager, getting height and depth on an overhead volley to earn break point. A long return in the next point undermines her efforts though, sending us back to deuce.
Stephens 4-6 *4-5 BartoliBREAK! Just as I was about to write off Stephens an eighth successive break of serve comes courtesy of an angled backhand winner up the line. A nice show of mental strength there from Stephens, but she must end this crazy sequence of breaks to stay in the match.
6.42pmConfident stuff from Stephens in a game she must win, driving to the net before swatting a volley aside with authority. Bartoli then smacks a low forehand into the net, gifting her opponent a 40-15 lead.
Stephens 4-6 5-5* BartoliAnd finally after nine attempts we have a hold of serve. Now this second set will get really interesting, with both players searching for a late breakthrough!
Stephens 4-6 *5-6 BartoliFrom one extreme to the next as Bartoli earns a comfortable hold to ease back ahead late in the second set. All the pressure now falls back under the American youngster, who must serve for a place in the match for a second time!
6.49pmMATCH POINTS! Stephens is in real trouble now after a second double fault, falling 0-40 behind and gifting Bartoli three match points.
Stephens 4-6 5-7 BartoliGAME SET AND MATCH! A forehand pass drifts long from Stephens, gifting the former finalist a straight sets win and a place in the semi-finals.
6.50pmA spirited, defiant effort from Stephens in her first Wimbledon quarter-final, but ultimately she could not match opponent's ferocious hitting at the baseline. I've no doubt that the 20-year-old will be back though, while Bartoli should provide a stern test in her third Grand Slam semi-final.
6.53pmThat just about does it for a pair of quarter-finals from Court One this afternoon, with a two-hour rain delay failing to prevent safe progress for Bartoli and Sabine Lisicki. Be sure to stick with Sports Mole for comprehensive coverage from SW19 all week. Good evening!