Ricardo Carvalho's second-half header prevented leaders Manchester United from going six points clear of Chelsea.
Saha celebrates his sixth league goal of the season
Louis Saha gave United a first-half lead after a wonderful piece of skill, bending the ball past Carlo Cudicini.
The game developed an intriguing ebb and flow in the second half as Saha twice went close, while Frank Lampard rained in a series of shots in reply.
And Carvalho earned Chelsea that point when he powered a header past Edwin van der Sar from a Lampard corner.
If United had the better of the first half, Chelsea were well worth the draw given their impressive second-half display.
Chelsea manager Jose Mourinho brought on Arjen Robben for Geremi at the restart, a switch that entailed Michael Essien dropping to right-back.
That formation provided Chelsea with greater attacking fluidity, with Essien superb in the way he surged forward from his defensive position.
The highlight of the opening half was Saha's exquisite goal.
When Rooney threaded a pass through to the Frenchman, with Carvalho and John Terry providing a defensive shield for Cudicini, there seemed minimal danger.
But Saha quickly switched the ball to his left foot, before bending a shot round Carvalho and past Cudicini's outstretched hand.
Given Saha had missed a penalty in United's Champions League defeat at Celtic in midweek, the French international has wasted little time in returning to the goalscoring groove as he claimed his sixth league goal.
The game had needed that moment of inspiration because the preceding 29 minutes had been overshadowed by some rugged physical approach from both sides.
That niggly tone was set by Michael Ballack's early challenge on Ronaldo.
The German soon found himself on the receiving end as he was sandwiched between Gabriel Heinze and Nemanja Vidic.
Not that the game was played in a mean spirit - early in the second half Rooney and Carvalho, who had last met in that infamous World Cup quarter-final in the summer, could be seen sharing a joke.
Chelsea had lots of possession in the first half but with Andriy Shevchenko and Didier Drogba tightly marked by Vidic and Rio Ferdinand their best efforts came from long-range shots.
Geremi hit a waspish shot that Van der Sar beat away and the Dutch keeper had to get down quickly to save a Lampard effort.
As Robben settled to the frenetic pace of the match, Rooney's run and cross almost created a second goal for Saha, who miscued as the ball came to him quickly.
Saha had another half-chance when Heinze's cross richocheted to the Frenchman, who again was unable to get a decisive touch.
On 70 minutes Carvalho's thumping header hauled Chelsea level.
The Portuguese defender rose above Heinze to meet Lampard's corner and Saha standing on the line was unable to divert the ball to safety.
Indeed Saha's headed intervention might have taken the ball away from Van der Sar, who had thrown himself to his right to try and save Carvalho's header.
With a quarter of an hour to go the anonmyous Shevchenko was withdrawn to replaced by Joe Cole, but the change failed to yield a winner for Chelsea.
Man Utd: Van der Sar, Neville, Ferdinand, Vidic, Heinze, Ronaldo (Fletcher 86), Carrick, Scholes, Giggs, Rooney, Saha (O'Shea 86).
Subs Not Used: Kuszczak, Evra, Silvestre.
Goals: Saha 29.
Chelsea: Cudicini, Geremi (Robben 46), Carvalho, Terry, Ashley Cole, Essien, Makelele, Ballack (Ferreira 90), Lampard, Shevchenko (Joe Cole 75), Drogba.
Subs Not Used: Hilario, Boulahrouz.
Booked: Makelele, Drogba, Ashley Cole.
Goals: Carvalho 69.
Ref: H Webb (S Yorkshire).