The Belgian headed in after Julian Speroni had parried his self-won penalty late in the first half to register his 19th goal of the season and carry Jose Mourinho’s side over the line with three games to spare.
Chelsea moved 16 points clear of outgoing champions Manchester City, who visit Tottenham Hotspur later on Sunday, and Arsenal, who travel to Hull City on Monday, meaning they can no longer be caught.
The title success, the club’s fifth in total, follows Chelsea’s triumph over Tottenham Hotspur in the League Cup final and sets the seal on a campaign they have dominated from start to finish.
The title-clinching win was characteristic of Chelsea’s gritty recent displays and it gave Mourinho the first league crown of his second stint at the club, as well as the eighth of his managerial career.
The Portuguese sent his side out with a succinct message in the match-day programme — “Three more points to be champions. Let’s do it together.” — but it took the hosts a while to get going.
With Didier Drogba dropping deep up front, Chelsea struggled to get in behind the visitors, who posed a threat on the break through the quicksilver dribbling of left-winger Wilfried Zaha.
When Chelsea did began to create chances, they found Palace goalkeeper Speroni in jittery form.
The Argentine was obliged to save at his near post from Nemanja Matic after failing to claim a Cesc Fabregas free-kick, while another set-piece saw him unconvincingly fumble away a shot from Drogba.
It required a trademark, full-bodied block from John Terry, meanwhile, to prevent Jason Puncheon giving Palace the lead, the ball flicking away off the Chelsea captain’s arm.
But on the cusp of half-time, Hazard, as he has done so often this season, supplied the breakthrough.
Despite minimal contact, James McArthur was adjudged to have impeded the Belgium forward in the penalty area as he burst onto Willian’s back-heel.
Hazard took the penalty himself and although Speroni blocked his initial shot — the first time he has failed to score from the spot in 10 attempts in the Premier League — he followed in to head home.
Chelsea’s fans spent part of the second half addressing odes to their club’s former stars, but Thibaut Courtois had to save decisively from Zaha before the champagne could be uncorked.
Palace have now lost three games in succession, but with survival long since secure, even their fans left the Bridge with smiles on their faces.