The Blues looked on course for the three points after Didier Drogba headed them into the lead with 52 minutes played.
However, United salvaged a share of the spoils when Van Persie smashed the ball in from close range with 60 seconds of added time remaining.
Read Sports Mole's minute-by-minute report below to find out how all of the action unfolded at Old Trafford.
3.01pmGood afternoon and welcome to Sports Mole's live text coverage of today's huge Premier League clash between Manchester United and Chelsea at Old Trafford. As always, this fixture is set up to be an explosive affair as two teams packed full of stars go head to head. We'll have team news for you in the next few minutes.
3.03pmMAN UTD: De Gea; Rafael, Smalling, Rojo, Shaw; Blind, Fellaini; Januzaj, Di Maria, Mata; Van Persie
3.04pmMAN UTD SUBS: Lindegaard, Blackett, Fletcher, Carrick, Herrera, A Pereira, Wilson
3.06pmThe big news for Man Utd is that Phil Jones and Radamel Falcao are both ruled out of today's match through injury. There were rumours beforehand that the duo were doubtful, and it has now been confirmed by the Red Devils. Louis van Gaal makes a total of two changes following on from Monday's 2-2 draw with West Bromwich Albion as Chris Smalling and Marouane Fellaini are both named in the starting lineup.
3.11pmChelsea manager Jose Mourinho claimed in midweek that Diego Costa had a "small chance" of being fit for today's game, but the Spain striker is not included in the squad for the visitors. Elsewhere, Mourinho has opted for two changes after seeing his side thrash Maribor 6-0 in the Champions League, with Didier Drogba and Gary Cahill being given the nod. John Obi Mikel and Andre Schurrle are among those on the bench.
3.14pmWith this being one of the biggest matches in the English football calendar, what's actually stake for the two teams this afternoon? Well, United can move up to fifth place in the table if they earn what would be a fourth win in six games. Meanwhile, Chelsea can extend their lead at the top of the table to six points if they leave Old Trafford with the spoils.
3.17pmMan Utd manager Louis van Gaal: "[Catching Chelsea] is possible. It is difficult to say, because I am then arrogant, but I have done it a lot of times, like at Barcelona. Chelsea is another level and then Manchester City also. But we have to see if we can beat them."
3.20pmChelsea manager Jose Mourinho: "We go to every match to win, but sometimes games go in one direction where in a pragmatic way you feel one point is good result. Sunday we go to win. If you give me now one point without me going I won't accept that. I want to fight for three points, but sometimes during a game a point is a positive result."
3.23pmThere has been a lot of mutual respect shown by both Van Gaal and Mourinho in the build-up to this match due to their previous partnership at Barcelona. Mourinho coached under Van Gaal at the Camp Nou in the late 1990s and the Portuguese has been eager to make it known that he owes the Dutchman plenty when it comes to his own managerial career. Meanwhile, Van Gaal has been claiming that Mourinho now towers above him when it comes to where they both stand in world football.
3.26pmUPDATE! Today's two early kickoffs in the Premier League have just finished and there have been plenty of goals in both. Burnley's misery near the foot of the table has continued with a 3-1 defeat at home to Everton, while Tottenham Hotspur have suffered a surprise 2-1 loss against Newcastle United at White Hart Lane.
3.29pmIt's a big day up front for Didier Drogba...
3.32pmHEAD TO HEAD: It's Man Utd who have the better record when it comes to past meetings between these teams, winning 68 games compared to Chelsea's 46. They have also played out a total of 49 draws, the most recent coming in this fixture last season as both sides failed to find the net.
3.35pmDespite Man Utd's better overall record, they've failed to beat Chelsea in their last four encounters with the Blues. The last time that the Red Devils came out on top against the Londoners was back in October 2012 with a 3-2 victory at Stamford Bridge in the Premier League. Meanwhile, Chelsea have won three out of the last six.
3.38pmFormer Man Utd defender Mikael Silvestre: "I think that this game is coming at the right time for Manchester United but it's going to be a real test of character. The players are slowly starting to understand each other a little better.
"For sure, Chelsea are the team to beat this season. They look so strong right now but I'm looking forward to seeing something positive from Manchester United this weekend."
3.41pmGot a spare couple of minutes before kickoff? Why not check out our video preview of today's match below:
3.44pmMan Utd goalkeeper David de Gea on opposite number Thibaut Courtois: "I saw him at Atletico Madrid. He played very well. He's a great goalie. He's young, he's big, he's a good shot stopper and he's good with crosses. He is one of the best."
You get the feeling that both men will play a big part in the outcome of today's match. Both men have been in superb form so far this season.
3.50pmTen minutes to go until kickoff and Old Trafford is filling up very nicely indeed. The Man Utd fans have not had a great deal to get excited about in the past 18 months or so, but you get the sense that their team is turning the corner now. That said, there can be no doubting that Chelsea will provide very tough opposition this afternoon. The Blues are flying at the moment, with an incredible amount of talent across all areas of the pitch.
3.55pmThe players are starting to emerge in the tunnel at Old Trafford and there are plenty of intense looks across their faces. John Terry stands proudly at the front of the Chelsea line, while Van Persie is at the front of the Man Utd line in the absence of the suspended Wayne Rooney.
1 minThe teams are out, the pre-match handshakes have been done, and it will be Man Utd to get us underway. The atmosphere inside the Theatre of Dreams is absolutely electric. Let's hope that today's match lives up to the hype. Here we go!
3 minChelsea carve out an early opening as Shaw gives the ball away on the edge of the box before Hazard's effort is deflected wide for a corner, which comes to nothing. The visitors win another corner soon after, only for Fellaini to head the ball powerfully away.
4 minCHANCE! Close to an opening goal for Man Utd as Mata's disguised pass finds its way to Di Maria, but the Argentine's volley flies over the crossbar. The big-money signing should have done better there, and the look on his face suggests that he knows it. It's been a very lively start.
7 minMan Utd are playing at a high tempo at the moment, giving Chelsea hardly any time on the ball. Fellaini in particular looks up for it this afternoon as he chases around in midfield.
10 minThe home fans are loving what they're seeing right now as the Red Devils continue to surge forward with pace. It feels like it's been a while since they've witnessed this kind of breathless counter-attacking football at Old Trafford. As for Chelsea, the visitors are seeing a decent amount of the ball, but they're lacking that killer touch in the final third.
12 minYELLOW CARD! The first booking of the afternoon goes the way of Rafael after he pulls back Hazard with the Belgian looking to run beyond him. The full-back is going to have to be very careful for the remainder of the game.
15 minChelsea ask a couple of questions of the Man Utd defence with a couple of corners, but the hosts do enough to see off the danger on both occasions. It's still fairly even out there, though you could probably argue that it's the hosts who are still marginally on top.
20 minFollowing that frantic opening, the game has settled down a bit now. Chelsea are enjoying a good spell, though Man Utd are still looking threatening on the counter-attack. The hosts win a free kick out on the right that Di Maria whips into a decent area, but Smalling can only head over.
21 minYELLOW CARD! Didier Drogba now goes into the book for a trip on Mata just as the Spaniard was looking to break upfield after a Chelsea corner.
22 minCHANCE! What a goal that would have been for the hosts, but Van Persie is denied by Courtois. Januzaj feeds the striker with a wonderfully incisive pass before his low drive is kept out by the Chelsea goalkeeper. That was a great stop.
25 minThe game has suddenly come to life again following that opportunity for Van Persie. It's breathless stuff at the moment as both teams surge forward at every available opportunity. Credit must go to Chelsea as well for not sitting back and trying to soak up the pressure: they're just as full of attacking intent as their opponents.
28 minChelsea see a good period of possession come to an end when Fabregas's ball over the top goes out of play for a goal kick. The midfielder hasn't been overly effective so far, though he's still providing his side with plenty of energy in the middle of the park and in advanced areas.
31 minWe've just had a bit of a break in play following a collision between Matic and Di Maria. However, the two men are now up and look okay to continue. Play resumes with Shaw and Januzaj trying to make something happen down the left, only for the move to break down.
34 minCHANCE! Chelsea break up the pitch with Willian, who races past Rojo before trying to take on Smalling. However, the England international stands his ground well to win the ball back for the home side. That could have been the opening goal of the game because Willian only had Smalling to beat before he would have been bearing down on De Gea.
37 minRafael does well to win a free kick on the right after it looked as if he had run into a dead end. Di Maria takes the resulting set piece, firing a good cross into the middle, but Courtois shows excellent composure to catch the ball.
38 minYELLOW CARD! Chelsea midfielder Nemanja Matic is the latest name to go into the book after he crashes into Van Persie. Clumsy stuff from the Serbian.
41 minSAVE! De Gea to the rescue for Man Utd, saving from Drogba on this occasion. The striker peels off his marker before hitting Oscar's cross towards goal, only for his effort to be kept out by the Spaniard. Man Utd then go up the other end with Januzaj, who lashes a fierce drive narrowly over the crossbar.
44 minCHANCE! Man Utd win a free kick on the edge of the box before Januzaj tees up Mata. The former Chelsea midfielder hits the ball first time towards goal, but his effort goes well over the crossbar from about 15 yards. That was a decent opening for the hosts.
4.48pmReferee Phil Dowd blows the half-time whistle, bringing an end to a riveting 45 minutes of football at Old Trafford. We've not had any goals so far, but there has been plenty of entertainment. Man Utd have had the better chances, though Chelsea have also threatened in the final third.
4.51pmLouis van Gaal is likely to be the happier of the two managers at the moment thanks to his side's energetic display. The Red Devils looked good going forward, while Marouane Fellaini has given them some bite in midfield.
4.56pmJose Mourinho will probably be feeling fairly satisfied with how his side performed in the first half, though the Blues left themselves far too open on a couple of occasions. Cesc Fabregas has been disappointing so far, failing to make a big impact in midfield.
5.01pmUPDATE! Today's two early kickoffs in the Premier League saw seven goals hit the back of the net as Everton beat Burnley 3-1 at Turf Moor, while Spurs lost 1-2 at home to Newcastle.
46 minSECOND HALF UNDERWAY! The teams are out for the second half and it will be Chelsea to kick us off. No changes from either manager at the break.
49 minIt's been a positive start to the second half for Chelsea, who are seeing plenty of the ball deep in Man Utd territory. Hazard is already giving the hosts a few things to think about. One attack causes some confusion inside the home side's penalty area, but the danger eventually ebbs away.
50 minYELLOW CARD! Chelsea midfielder Fabregas goes into the book at the start of the second half for a clumsy challenge on Mata.
51 minCHANCE! Fellaini almost scores his second goal in as many games for Man Utd as he is teed up on the edge of the box by Van Persie. However, the Belgian doesn't connect properly and his shot flies narrowly wide of the post.
52 minChelsea take the lead and it's Didier Drogba with the goal! The visitors win a corner following a superb save from De Gea to deny Hazard, but Man Utd fail to defend the set piece as Drogba gets above his marker to flick a deft header into the net.
55 minThe wind seems to have been taken out of the Man Utd sails a little bit following that goal. The hosts have been excellent for large parts of the match, but they are now looking a bit more cautious when in possession.
60 minAn hour played at Old Trafford and Chelsea are looking in control. Man Utd's caution is allowing the visitors to enjoy more time on the ball. The hosts don't want to concede again any time soon, so they are happy to keep the Blues at arm's length. Willian gets a sight of goal from about 25 yards, but De Gea saves comfortably.
62 minYELLOW CARD! Chelsea midfielder Oscar now goes into the book following a clumsy tackle on Smalling.
65 minCHELSEA SUB: The visitors make their first change of the match as John Obi Mikel replaces Oscar.
66 minMAN UTD: Now it's Man Utd who shake things up as youngster James Wilson is introduced in place of Juan Mata.
68 minCHANCE! What a goal that would have been from, of all people, Ivanovic! The defender dances his way through the Man Utd defence before firing just wide of the far post. The visitors are cranking up the pressure here, sensing that a second goal is within their grasp.
71 minThe Blues are continuing to camp out in the Man Utd half, probing away around the edge of the penalty area. Hazard in particular is giving the hosts a headache with his clever runs and all-round trickery. Man Utd have just under 20 minutes of normal time remaining to get themselves back in this game.
74 minMore and more gaps are opening up around the pitch as this match heads towards the final 10 minutes. From a Man Utd perspective, the hosts are looking a little bit short of ideas.
77 minYELLOW CARD! An easy decision for Phil Dowd as he books Marouane Fellaini for pulling back Hazard. Time is running out for the Red Devils, though they will feel as if a positive result is still possible.
78 minCHANCE! Van Persie has a sniff of goal again as he is slipped in by Shaw, but the Dutchman's low shot on the angle is well saved by Courtois. That seems to have livened the Man Utd fans up a bit. The hosts carve out another opening moments later, only for Januzaj to slice wide from the edge of the box.
81 minChelsea are trying their best to exploit the spaces that Man Utd are now leaving as we enter the final 10 minutes at Old Trafford. It's very hard to predict what's going to happen next because it remains fairly end to end.
84 minMan Utd win themselves a corner after good work down the left from Januzaj, but the youngster's delivery is easily held by Courtois. That was poor from the Belgian. Chelsea will just be grateful to get back in possession and dictate the pace of these final few minutes.
87 minYELLOW CARD! Hazard goes into the book now after dragging Rafael down out in a wide position. Di Maria whips the resulting free kick into the box, but the whistle goes for an infringement involving Januzaj and Ivanovic.
89 minCHELSEA SUB: The visitors run the clock down with another change as Eden Hazard is replaced by Andre Schurrle.
90 minThere will be FOUR MINUTES of added time at Old Trafford...
90+2 minCHELSEA SUB: Another Chelsea swap sees Kurt Zouma enter the action in place of Willian.
90+3 minRED CARD! IVANOVIC (CHELSEA) Chelsea will end the game with 10 men as Branislav Ivanovic is sent off after picking up a second yellow card for a foul on Di Maria.
90+3 minCan you believe it?! Man Utd get their equaliser from the resulting free kick, with Van Persie smashing the ball in from close ranger after Fellaini's initial effort had been brilliantly saved by Courtois. What an incredible finish at Old Trafford!
5.56pmWhat a finale at Old Trafford. The game ends 1-1 as Van Persie's late goal salvages Man Utd a precious point. Chelsea will be gutted that they weren't able to hold on.
5.57pmThat's all from our live coverage of today's match, but be sure to catch up with all of the reaction from both camps right here on Sports Mole. Thanks for your company, we hope to see you again soon. Goodbye!