John Terry headed the hosts in front early on, before Steven Gerrard equalised shortly before half time.
The visitors enjoyed more of the possession in the second half and Philippe Coutinho went close as he fired wide, but Liverpool couldn’t find the winner they needed to close the gap on Manchester United in fourth.
The result means Jose Mourinho continues his unbeaten record against Liverpool, and leaves Brendan Rodgers??? men six points off fourth place with two games left, effectively ending their Champions League hopes owing to their inferior goal difference.??
Liverpool afforded the newly crowned champions a guard of honour as they came on to the pitch, but Chelsea were in no mood to relax and Cesc Fabregas came out firing, catching Raheem Sterling with a late challenge to earn a booking inside the first minute.
The visitors then allowed Blues skipper Terry too much space in the box from Cesc Fabregas??? corner, with the defender rising above Rickie Lambert to power a header into the corner as Simon Mignolet and Gerrard failed to keep it out, and Chelsea were ahead inside five minutes.
The party spirit was in full swing as Chelsea looked more expansive than in their recent matches, with the pressure of securing the title lifted from their shoulders.
But Liverpool had something to play for and enjoyed some spells of possession, with Philippe Coutinho going close with a couple of efforts, his first deflecting wide off Filipe Luis from 20 yards before he cut inside Kurt Zouma and saw a low shot saved by Thibaut Courtois.
For most of the half Chelsea looked comfortable and the visitors were struggling with the threat of Mourinho???s men down the left flank, but they drew level after Branislav Ivanovic was booked for hauling down Adam Lallana near the corner flag in the 44th minute.
Jordan Henderson whipped in the resulting free kick and Gerrard popped up unmarked at the far post, nodding it down into the net to level things right before the break.
The visitors started the second half the brighter of the two sides, and Coutinho had a glorious opportunity to put his side in front, but he could only fire his first-time shot wide of the post after good work by Raheem Sterling down the left.
Willian had a couple of chances in quick succession for the hosts, drilling one shot just wide of the far post from a tight angle before seeing a second effort diverted behind by Martin Skrtel from the same position.
The hosts introduced Nemanja Matic on the hour mark, and Chelsea almost immediately looked more solid in the middle of the park, but Liverpool were still seeing plenty more of the ball.
Chelsea were creating some good openings, though, and Cesc Fabregas bundled his way through the Liverpool defence before firing a low left-footed effort, only to see Skrtel make another excellent last-ditch block.
Coutinho???s deflected effort was saved by Courtois late on, while Jordan Henderson fired an 18-yard volley wide of the target, with neither side able to find the winner, leaving Liverpool six points adrift of Manchester United with an inferior goal difference with two games remaining, meaning their Champions League aspirations are pretty much over.
Rodgers’ men next face Crystal Palace as Gerrard prepares for the emotional occasion of his last match for Liverpool at Anfield.