It stretched Chelsea's unbeaten sequence in the Premier League at Stamford Bridge to 85 games, but Sir Alex Ferguson will be frustrated that his side failed to build on a perfect start and lost their way as the game went on.
Chelsea will be delighted and relieved with a point - but they should have claimed all three after dominating the second half.
United opted to keep Cristiano Ronaldo on the bench, where he was joined by Carlos Tevez as Berbatov and Wayne Rooney were paired up front.
Chelsea were forced into a reshuffle of their own when Deco injured a thigh in the warm-up, although they were hardly weakened by the subsequent inclusion of Michael Ballack.
Scolari views draw as a point won
United opened with real purpose, Darren Fletcher scrambling a finish wide and Rooney hooking just off target after a poor clearance from Cech.
Chelsea had a chance of their own in the eighth minute when Joe Cole ran clear after appearing to use his hand, only to shoot wide.
Luiz Felipe Scolari's side suffered a serious blow three minutes later when defender Ricardo Carvalho departed with a knee injury, with Alex coming on as substitute.
United's ambition was rewarded with a deserved opener after 18 minutes, when Park pounced from close range after Cech could only parry Berbatov's shot.
Van der Sar had been having a mixed afternoon, his mood not helped by a knee injury sustained in an accidental clash with Florent Malouda.
And it was no surprise when he limped off and was replaced by Tomasz Kuszczak after 31 minutes following another fumble.
Park delighted to score opener
Kuszczak was quickly in action to block a long-range effort from Alex, but the game was degenerating into a scrappy affair littered with stoppages.
Chelsea made another change at the interval, sending on Didier Drogba for Malouda, while United waited until nine minutes after half-time before sending on Ronaldo for Paul Scholes.
Joe Cole wasted another great opportunity after 65 minutes, shooting straight at Kuszczak after being released by Ballack's superb pass.
And Anelka was guilty of a shocking miss seven minutes later when he was set up by Joe Cole, but he failed to even apply a touch only three yards out with the goal at his mercy.
But Chelsea were building up a head of steam and it was no surprise when they drew level with 10 minutes left.
Rooney was booked for a crude lunge at Ashley Cole, and the punishment was doubled when Kalou headed Jon Mikel Obi's free-kick beyond a static Kuszczak.
And it took a desperate block from Gary Neville seconds later to deny Kalou, bravely deflecting his shot over the top as United hung on for a point.
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