Visiting United controlled large parts of the first half, but found themselves behind after 36 minutes. Chelsea winger Daniel Sturridge jinked his way past Patrice Evra before sending in a cross which bounced off United defender Jonny Evans and into his own net.
Ashley Young had United's best chance to draw level before the break, but his curling effort was palmed wide by Chelsea goalkeeper Petr Cech.
Hosting Chelsea came out for the second half in positive mood and found themselves three goals to the good by the 50th minute.
United's first goal of the afternoon came in the 58th minute when Evra's run into the area was halted by foul from Sturridge. Wayne Rooney stepped up to convert the resultant spot-kick.
United were now in the ascendancy and eventually claimed the equalising goal in the 84th minute. Rooney's initial shot was parried by Cech, but Ryan Giggs was on hand to collect the rebound and cross for substitute Javier Hernandez to head in from close range.
Both sides created chances to take maximum points, with the Mata going the closest for Chelsea after seeing his goalbound free-kick tipped wide by De Gea.