Three points were needed and three points were duly achieved and Chelsea are the champiions once again.
It might have taken a header from a saved spot kick just before half time by Hazard to break the Eagles resistance, but it was enough and the wild cheers sang from the rafter as referee Kevin Friend blew his whistle at the end.
Dazzling blue streamers greeted the players as they took the applause from the adoring Chelsea faithful.
The awarding to the trophy will have to wait until the end of the last game of the seasons at home to Sunderland.
This was not a vintage, expansive performance from Chelsea and Palace played their part in pushing the Blues to the limit, but it was enough.
Chelsea forced the early pace and Didier Drogba was unlucky not to get his head to a fine chip by Cesc Fabregas. The south Londoners, undaunted at the prospect of playing second fiddle to the champion-elect upped the tempo themselves.
An ambitious 30-harder by Juan Cuadrado, drafted in off the bench following the late withdrawal of Ramires, failed to trouble Juilan Speroni on 16 minutes.
Speroni spilled a viscous dipping free-kick by Drogba on 26. Unfortunately for the Blues no one was following up to take advantage of the loose ball.
Palace had a great chance to take the lead on 30 minutes. Some magic from Wilfred Zaha, on the left saw John Terry slip allowing Jason Puncheon to thump the ball goal-bound. Terry dived to thwart the striker and the ball appeared to hit the Chelsea skipper's hand before being cleared.
With three minutes untill the break, and after a cheeky back heel by Willian, Hazard raced into the Palace penalty are an ad was upended by James McArthur.
The midfielder took the ok kick which was brilliantly saved by Speroni but the ball fell invitingly back to Hazard who headed the ball into the net for his 19th goal of the season.
Jose Mourinho replaced ineffectual Cuadrado with Mikel at the break.
Eagles boss Alan Pardew decided to ring the changes with the introduction of Martin Kelly and Glenn Murray. They replaced Adrian Mariappa and Jordon Mutch on 60 minutes.
As shot by Puncheon inched just wide of Thibaut Courtois's goal as the Eagoes went in seasick of a deserved equaliser. That was the last action for Puncheon as he was substituted for Yaya Sanogo a minute later.
However the long ball option deployed by Pardew failed to reap even a single shot on goal with 10 minutes left on the clock. Instead a second of. chelSea seemed more likely with half chances falling to Mikel, Ivanovic, Drogba and Willian.
Mourinho, perhaps sensing another goal just would not come, opted to bring on defender Kurt Zouma for winger Willian with just five minutes away from being proclaimed champions.that five minutes duly came and the best team in the country this season fully deserved the accolade of Premier League champions.
Teams: Chelsea, Courtois, Ivanovic, Fabrehas, Cuadrado, Hazard, Drogba, Matic, Willian, Cahill, Terry, Azpilicueta
Subs, Cech, Luis, Zouma, Mikel, Remy, Ake Loftus-Cheek
Palace, Speroni, Ward, Mariappa, Dann, Bolasie, Zaha, McArthur, Mutch, Delaney, Ledley, Puncheon
Subs, Hennessey, Hangerland, Sanogo, Jedinak, Murray, Chung-Yong, Kelly
Referee Kevin Friend