United dominated the first half, while Chelsea recovered to win the second and leave the Londoners second in the table behind Arsenal.
Darren Fletcher had the first chance of the match on five minutes when he volleyed a Owen Hargreaves right-wing cross from just inside the Chelsea penalty wide of Petr Cech's post.
Three minutes later and a poor clearance by Cech left Dimitar Berbatov to lob the ball to Wayne Rooney, whose audacious volley just missed the Chelsea goal.
Chelsea responded seconds later but Joe Cole missed a sitter to put the Blues one up when he raced clear only to see his right-foot drive smash the side-netting rather than the back of the net.
Having lost Deco minutes before the start of the match with a hip problem, Chelsea were forced into an early change bringing on Alex for Ricardo Carvalho.
Cech was forced into a fantastic save to halt United on 16 minutes when a fine counter-attack from the visitors saw Rooney open up the Chelsea defence and pass the ball to Rio Ferdinand.
His crisp right-footed drive was deflected from goal by Cech's outstretched right foot.
But the inevitable occurred half a minute later when first Patrice Evra found Berbatov, who saw his shot saved by Cech but Park side-footed the ball home under the keeper's body to put United one up.
United replaced the injured Edwin van der Sar on 33 minutes with Tomasz Kuszczak.
The replacement was in action on 40 minutes when he failed to hold an Alex piledriver and the ball was cleared.
Nicolas Anelka had a chance to level the score five minute from the break but his right-footed shot was wayward and it sailed over the United crossbar.
Didier Drogba replaced Florent Malouda at half-time to pep up Chelsea's attack.
Cristiano Ronaldo replaced Paul Scholes on 55 minutes and his first touch saw a whipped left-footer from just outside the Chelsea area fly inches wide of goal.
Joe Cole had the perfect chance to level on 66 minutes when Michael Ballack opened up the United defence.
Cole raced through of the left but his left-footed drive was straight into the body of Kuszczak.
With 17 minutes remaining, a Joe Cole low cross needed only for Anelka to touch it to score but the Frenchman completely missed the ball from three yards out.
But it was substitute Kalou who levelled the scores with a wonderful header 10 minutes from time.
He had only been on the pitch for five minutes when, completely unmarked from a deep John Obi Mikel free-kick, he planted the ball wide of Kuszczak's outstretched right hand.
Chelsea pushed United back in search of the winner, but the visitors hung on for a valuable point.