Despite dominating for long periods, United's Stamford Bridge curse looked to have struck again when Jonny Evans put Daniel Sturridge's cross into his own net, Juan Mata scored a superb goal and a David Luiz header flew in off the shoulder of Rio Ferdinand.
But the champions were awarded two penalties, both convered by Rooney, before substitute Javier Hernandez headed home a Ryan Giggs cross to earn the champions a share of the spoils.
It was more dropped points for Chelsea from a winning position as they almost lost at home in the league to United for the first time in 10 years.
Even though he was not playing, John Terry cast a long shadow over proceedings, with the visiting supporters taunting him over his highly-publicised problems.
Chelsea fans predictably showed their backing with chants of "There's only one England captain", while jeering Rio Ferdinand's every touch.
They also had plenty of fun at the expense of David De Gea, who was making his first league appearance of 2012 and whose edginess was betrayed in the eighth minute when he flapped at a cross.
But it was Chelsea who were soon breathing a sigh of relief as two United penalty cries were ignored.
The first saw Ashley Young go down rather easily under pressure from Jose Bosingwa, who got the nod at left-back with Ashley Cole suspended.
Moments later, Danny Welbeck went down after being caught by the trailing leg of Chelsea debutant Gary Cahill, an outraged Sir Alex Ferguson racing onto the pitch as Howard Webb ignored the United appeals.
Replays appeared to show Cahill had won the ball before catching Welbeck, but the decision only fuelled a poisonous atmosphere that included more abusive chants about Terry and Ferdinand.
The football did little to lift the mood until just before the half-hour when Branislav Ivanovic just beat Welbeck to Rooney's cross after a wonderful ball from Antonio Valencia.
Webb brandished his yellow card when Fernando Torres ran into the back of Evans, for whom insult was added to injury nine minutes before half-time when he inadvertently gave Chelsea the lead.
United failed to clear their lines and the ball broke to Sturridge, who got past Evra to the byline and fired in a cross that hit De Gea and then went in off Evans' arm.
Sturridge's vicious drive was repelled by De Gea before Petr Cech was finally called into meaningful action when he got fingertips on Young's curler.
The Chelsea goalkeeper then produced an even better stop on Welbeck's snapshot and Ivanovic was booked for running into Young as United finished the first half on top.
Ferguson had complained in his pre-match interview that the away dressing room was frigid enough to "hang meat in" and the visitors were certainly caught cold at the restart as the home side trebled their advantage inside five minutes.
The second goal took less than 30 seconds, Torres getting clear down the right and whipping in the perfect cross for Mata to lash home a wonderful volley before De Gea could even move.
If that was sublime, the third was unlucky again for United, with Luiz heading Mata's free-kick against the shoulder of Ferdinand and into the net.
However, United, who threw on Hernandez for Young, enjoyed a spectacular reversal of fortune when they were awarded two penalties inside 10 minutes.
The first saw Sturridge adjudged to have knocked over Evra, with Chelsea boss Andre Villas-Boas launching a bottle into the advertising hoarding in disgust before Rooney stepped up to blast the penalty into the top left-hand corner.
Juan Mata and Rooney tested the goalkeeper at either end and Paul Scholes came on for Rafael before Webb pointed to the spot again when Welbeck tripped over the leg of Ivanovic.
This time Rooney went to Cech's left to put United within one goal of another astonishing comeback.
And although Oriol Romeu came on to shore things up and De Gea produced another uncomfortable punch on Michael Essien's drive, Ferguson's men deservedly equalised six minutes from time.
Cech could only parry Rooney's shot out to Ryan Giggs on the left and the veteran crossed for the unmarked Hernandez to head straight through Cech.
Raul Meireles almost snatched it for Chelsea when he nodded Florent Malouda's cross over the top and De Gea produced two stunning stoppage-time saves to keep out Mata's free-kick and Cahill's drive.