The Argentine started quickly and broke serve in the opening game, wrapping up the first set in ruthless fashion soon after.
Levine showed spirit to fight back in the second set, eventually losing in a tense tie-break to the eighth seed.
Del Potro kept the pressure on and secured a straight-sets win in just over two hours.
Look back at a confident display from the former Grand Slam champion with Sports Mole's live coverage below.
12.57pmAfternoon tennis fans. A quite memorable start to Wimbledon 2013 has seen seeds fall at an alarming rate. Day four of our coverage will start with another top seed looking to avoid an early exit, with Juan Martin del Potro taking on Jesse Levine on Centre Court.
12.59pmDel Potro will be acutely aware of the need to show form and focus today, after watching Rafael Nadal and Roger Federer dumped out against unheralded players earlier this week. The fourth seed takes on Canadian left-hander Levine to start a full day's play on Centre, looking for safe passage into the third round.
1.02pmLevine has it all to do this afternoon against the fourth seed, with Del Potro looking calm and composed in a straight-sets first-round victory on Tuesday. The Argentine has never been beyond the fourth round at SW19 and will surely be desperate to put that right in 2013, with the men's draw looking fairly open from top to bottom.
1.05pmDel Potro is currently on course for a quarter-final showdown against David Ferrer, but given the unpredictable nature of this tournament who know what the next 10 days have in store. The eight seed is in the top of a draw dominated by Novak Djokovic, which means Federer's exit yesterday should have little direct impact on his efforts this year at SW19.
1.08pmBoth players are due on Centre Court in a matter of moments, kicking off a packed schedule in the showpiece arena which also includes matches featuring Djokovic and Agnieszka Radwanska.
1.11pmIn truth Del Potro should have enough power and poise to progress with relative ease to the third round, but the giant Argentine has stumbled at Wimbledon before in the early rounds. Injury has unfortunately scuppered his attempts to build on that US Open in 2009, but with the draw so open this year he definitely has to be considered a contender for the title.
1.13pmWe are just about ready to get underway on Centre Court, with Levine to serve first on the near side. He opens things up by winning a cheap point on serve, with Del Potro shaking off the cobwebs by aiming a forehand wide of the line.
1.15pmBREAK POINTS! A clear sign of early jitters on serve for Levine as he sends a stray backhand to the net, conceding two break points at 15-40 in the process.
Del Potro *1-0 LevineBREAK! A poor start for Levine in his debut on Centre Court, with a baseline exchange ended abruptly with another unforced error from the Canadian. The opening game ends with a swift break for Del Potro, who takes charge almost from the outset.
Del Potro 2-0* LevineDel Potro wastes no time in stamping his authority on serve, showing his awesome power with a precise forehand winner across court. Levine is then simply unable to keep successive first serves in, allowing the Argentine to consolidate that early break.
1.18pmA welcome show of strength from Levine on serve as he shows some sign of settling down, winning a pair of points to start his second service game. Del Potro is quick to expose a poor volley at the net though, calmly wrapping a clever forehand winner down the line to earn a break-point chance at 30-40.
1.21pmLevine survives at break point with a gutsy play at the net, but once again looks nervous with a slack forehand that fails to stay in play. Back to deuce in a game you feel the Canadian desperately needs to build confidence early in the match.
Del Potro *3-0 LevineBREAK! A horrible double fault is followed by a confident ace for Levine, who sums up his inconsistent style in those two points perfectly. At deuce another error creeps in serve for his second double fault, gifting Del Potro his fourth break-point chance, but his troubles on serve are not over. Make that three double faults in four points for the Canadian, who really is struggling to deal with this occasion so far today.
Del Potro 4-0* LevineA routine hold sees Del Potro came his fourth successive game inside 16 minutes. We need to see more from Levine on serve quickly for this match to become competitive.
Del Potro *4-1 LevineMuch more like it from the Canadian and a hold to love finally gets the underdog on the board in the first set. A couple of sloppy forehand returns from Del Potro definitely helped but that was a much more aggressive showing from Levine, who will surely look to regroup now for a push in the second set.
1.32pmEach time these two players have shared a baseline exchange so far Levine seems to buckle, failing to return fairly simple backhands with time to pick his spot. The Canadian is a far better player than he has shown so far, with Del Potro showing strong movement to ease round the court and control each point.
Del Potro 5-1* LevineA decent attempt to mix things up from Levine with a short shot into the net, but Del Potro reads his intentions and clubs a forehand winner into the far corner. A quick ace then follows and keeps the eighth seed's double break intact, with Levine forced to serve to stay in this first set.
Del Potro *5-2 LevineDel Potro shows superb defence to chase down an array of shots deep at rhe baseline, winning a point at 40-15 on the Levine serve in the process. The Canadian then chases down a short forehand for a timely hold under pressure, but Del Potro is still an overwhelming favourite to claim this first set shortly.
1.40pmBREAK POINTS! Nothing to lose in this game for Levine and he starts it brightly, skewing a forehand winner across court. Del Potro then allows a deep baseline effort to fall long after an untimely slip, which makes it 15-40 and a first chance to the break for the Canadian.
Del Potro 6-2* LevineSET! Del Potro plays to his strengths and staves off both break points, using a massive 130mph serve to finish create a set point after edging back to deuce. Levine lets a slice fly long and in just over 30 minutes Del Potro has a set on the board.
1.46pmYou feel that this opening service game of the second set is absolutely vital for Levine and he starts it with style, hitting a drop shot to perfection at the net. We need to see more variety along those lines from the Canadian to take Del Potro out of his comfort zone.
Del Potro 6-2 *0-1 LevineMuch more like from Levine as he uses speed around the court to claim a vital hold. Another quick dart to the net saw the Canadian win by far his most promising point of the match in that game, using quick footwork to slice a clever volley at the net.
Del Potro 6-2 1-1* LevineThe first hold to love for Del Potro features a pair of those trademark thunderous serves up the line, restoring parity early in the second set.
1.52pmA fifth double fault sees Levine back under pressure in his next service game, with a forehand winner crashing well past the baseline to bring Del Potro level at 30-30. The Canadian really needs to dig deep and grind out a hold but once again falters with an unforced error, volleying out at the net to give his opponent break point.
Del Potro 6-2 *1-2 LevineStrong work on the left-hander's backhand side helps Levine battle back to hold. Del Potro had a challenge ruled against him at deuce and failed to recover, with Levine smashing a welcome ace down the middle to keep this second set on serve.
1.57pmBREAK POINT! Levine puts his opponent's serve under relative pressure and earn a huge break-point chance, with Del Potro just unable to make a deep forehand down the line. What a chance for the Canadian to make a statement of intent early in the second set.
Del Potro 6-2 1-3* LevineBREAK! Del Potro sends a forehand wide and with it concedes a break of serve. A real show of character from Levine after that shaky start to earn a foothold in the second set. Very important now for the world number 112 to consolidate by holding in the next game.
2.02pmBREAK POINT! Almost instantly Del Potro earns a chance to break back. The Argentine showed superb defence to keep a gruelling baseline exchange alive, with Levine unable to make a slice count at the net.
Del Potro 6-2 *1-4 LevineWhat an effort from Levine to rally and claim a hold he desperately needed, consolidating his advantage in the second set. Both players traded shots in a magnificent exchange to finish the game, but after moving Del Potro inside a sublime forehand pass deep in the corner proved too good for the eighth seed, who now knows that he has a fight on his hands this afternoon on Centre Court.
Del Potro 6-2 2-4* LevineDel Potro quickly gets in trouble in his first point back on serve, but bails himself out with a ferocious forehand down the line. The Argentine clearly looks agitated and responds with sheer power, smashing a first serve down the middle for the hold.
2.11pmA huge backhand peppered down the line from Levine exposes a short return at 30-30 but Del Potro quickly puts it right, smashing a forehand return up the line to level things up at deuce.
Del Potro 6-2 *2-5 LevineOnce again Levine finds a way to make his service game stick against the odds, favouring a powerful backhand shot that keeps finding the line consistently. Del Potro will serve to stay in the second set shortly.
Del Potro 6-2 3-5* LevineA second hold to love helps Del Potro stay alive in the second set, putting all the pressure back on Levine's shoulders. Rather unfortunately for Levine its time for new balls, giving his powerful opponent the chance to thunder back returns with just a little more zip.
2.18pmLevine challenges a call on the right baseline but to no avail, with the ball bouncing out by just a matter of inches. That stroke of fortune gives Del Potro a 15-30 lead but the Canadian is quick to respond, driving inside at speed to level a vital game.
2.20pmBREAK POINT! Somehow Levine survives break point as the gets the better of a memorable exchange at the net. Del Potro comes inside but neglects to clatter a volley directly at his opponent, paying the price as a lob flies over his head and bounces inside the baseline.
Del Potro 6-2 *4-5 LevineBREAK! Just one error to many for Levine on serve, with Del Potro punishing a sloppy second serve to earn a break that keeps the set well and truly alive. The Canadian desperately needed to close out that service game but couldn't find the shots required under pressure.
Del Potro 6-2 5-5* LevineRuthless serving from Del Potro levels the second set to love. That was all to easy for the Argentine as smacks a serve down the line at 128mph for an easy hold. You just sense that the match will be won and lost for Levine on the strength of this second set.
Del Potro 6-2 *5-6 LevineMore aggression from Levine pays off to keep the second set on serve. Del Potro was definitely too cautious at the baseline and got exposed, with the highlight of a routine hold a thumping backhand winner into space.
2.28pmAnother peach of a backhand helps Levine claim a foothold on Del Potro's serve at 0-15, but Del Potro steps inside to win two points in quick succession.
Del Potro 6-2 6-6* LevineA rocket serve from Del Potro warps up a necessary hold for the Argentine, sending the second set into a tie breaker.
2.32pmAn early mistake in the breaker from Del Potro, who falls 3-0 behind after getting his angles wrong with a soft forehand taken far too early. What a chance this is for Levine to claim a second set he probably just deserves on balance.
2.34pmLevine buckles slightly and gets his tactics wrong in a pair of baseline exchanges, bringing Del Potro firmly back into the breaker at 3-2. A gutsy move inside then forces a mistake from Del Potro, giving the Canadian a 4-2 lead at the change of ends.
2.36pmSupreme shot-making on his forehand side helps Del Potro recover to make the score 4-4 in this vital breaker. Levine then makes a horrible error at the baseline and before he can blink is staring at a 5-4 deficit after losing three consecutive points.
2.38pmSET POINT! Del Potro earns set point by battering first serve up the middle, but once again Levine fight hard and hangs on with a backhand volley at the net. His joy is shortlived though as another unforced error at the baseline gives Del Potro his second set point.
Del Potro 6-2 *7-6(7) LevineSET! At the third time of asking Del Potro makes his chance to claim the second set count. The Argentine showed his class to crush a 134mph serve across court, before a forehand pass proves too strong for Levine at the baseline.
2.44pmLevine fought and was desperately unlucky not to take that second set, but just failed to show composure after working so hard to serve for the chance to bring this match level. The Canadian has never won a five-set match and his tasks looks extremely difficult to change that this afternoon.
2.48pmBREAK POINTS! Brute force on Del Potro's forehand is enough to earn two more break points. Levine has just lost that edge and variety that made a dent in his opponent's play early in the second set.
Del Potro 6-2 7-6(7) *2-0 LevineBREAK! A noticeable increase in tempo from Del Potro is enough to take control of the third set, with Levine just failing to chase down a makable shot at the net. The Canadian now looks resigned to his fate and needs to go for broke.
Del Potro 6-2 7-6(7) 3-0* LevineIn the last 10 minutes Del Potro has found a gear his opponent just cannot live with. A huge scream greets a powerful forehand across court from the Argentine, sending his opponent the wrong way and consolidating his break as a result.
2.55pmLevine recovers come composure to aim a worthy baseline winner off the sideline as he looks for a way back into the third set. Del Potro decides to challenge a baseline call in the next point and his effort proves worthy, the ball was in and the point will be replayed. The Argentine wants the point outright and argues with the umpire, but to no avail.
Del Potro 6-2 7-6(7) *3-1 LevineThe Canadian keeps the third set competitive with an effective slice serve, with Del Potro still holding that advantage claimed by an early break.
Del Potro 6-2 7-6(7) 4-1* LevineThis match could be over shortly if Del Potro keeps his serving to that standard. A missile down the centre helps him claim a routine hold and move within two games of earning a place in the third round.
Del Potro 6-2 7-6(7) *4-2 LevineAt last a decent drop shot from Levine, taking the big man's physical advantages away with an accurate strike just over the net. That point proved the catalyst for a hold to love, just about keeping the Canadian alive in this third set.
Del Potro 6-2 7-6(7) 5-2* LevineMore punishing first serves help Del Potro close to within a game of progression, but Levine played his part by edging a 28-shot rally to start the game. His efforts were not good enough though and he must now serve to hang on just a little bit longer on Centre Court.
Del Potro 6-2 7-6(7) *5-3 LevineDel Potro will have to serve the match out after a mix of strong serving and backhand winners get the job done for Levine. The Argentine looks in a hurry to finish this up now though, so expect more mammoth first serves when play resumes.
Del Potro 6-2 7-6(7) 6-3 LevineGAME SET AND MATCH! Levine gifts his opponent match point with a loose backhand return and Del Potro needs no second invitation, launching his 14th ace down the line to complete a straight-sets win.
3.11pmDel Potro looks to be building confidence and survived a little scare in the second set from Levine, coming through in just a minute over two hours. The eighth seed now advances to the third round, where he will probably play Grigor Dimitrov.
3.14pmThanks for following the giant Argentine's progress, and be sure to join us in just a few moments for continues live coverage from Centre Court. Good afternoon!