Despite both sides' best efforts, the pair were unable to capitalise on Manchester United's defeat earlier on in the day.
Liverpool almost took the lead within two minutes. A lovely ball by Jermaine Pennant found John Arne Riise in acres of space, but his poor first touch allowed the ball to roll harmlessly into Petr Cech's arms.
The game came to life in the 16th minute and it was Liverpool's record signing, Fernando Torres, who carved out the opening goal.
A great ball from Steven Gerrard split the Chelsea defence and left Torres in a one-on-one situation with the Blues centre-back Tal Ben Haim.
The Spanish striker took the ball in his stride and held off Ben Haim's challenge with ease before slotting a beautiful right-footed shot past Cech.
Liverpool ended the half at 1-0 up and were looking good value for their lead.
But Chelsea started the second half with a bang and substitute Claudio Pizarro should have levelled things for the Blues.
Salomon Kalou had made way for Pizarro and within three minutes of the restart the Peruvian replacement spurned a glorious chance.
A 30-yard ball by John Obi Mikel was picked up by Shaun Wright-Phillips on the wing, who whipped a cross into Pizarro, but despite being unmarked his free header sailed wide much to the relief of the Anfield faithful.
A minute later Chelsea were back on level terms thanks to a controversial penalty decision from referee Rob Styles.
A ball from across the box by Wright-Phillips was heading towards Florent Malouda. The Frenchman let the ball run through his legs and went to ground as Steve Finnan made a challenge on the edge of the box.
England midfielder Frank Lampard stepped up to send Jose Manuel Reina the wrong way and levelled the scores at 1-1.
Liverpool tried in vain to regain their lead and brought on dynamic Dutch winger Ryan Babel for the lively Pennant with 20 minutes left to play.
But the game fizzled out into a draw, with neither team having to deal with the psychological blow of losing.