The history makers got off to a slow start on the final day by conceding early on to a rare Javier Manquillo strike, but Willian got them back on track and four more goals - two from substitute Michy Batshuayi - followed in the second half to add some sparkle to the scoreline.
The contest had an almost testimonial feel to it at times, with Chelsea wrapping up the title with time to spare and Sunderland already confirmed to go down as the bottom-placed side, giving Antonio Conte the chance to give John Terry a rather choreographed send-off.
When 26 minutes had elapsed Conte brought long-serving skipper Terry off, bringing an end to his 22-year Stamford Bridge association on what was likely his 717th and final outing for the club.
Prior to that, the Black Cats were ahead with just a few minutes on the clock, capitalising on some slack defending at the back from Chelsea as Manquillo rifled the ball past Thibaut Courtois after a deflected free kick fell kindly to him.
Having failed to score in 11 of their last 13 matches, it was a rare occasion for the travelling fans to smile, but their joy lasted for all of five minutes before Willian found a way through to level things up.
The move began with Marcos Alonso sending his free kick against the upright and, after the visitors failed to clear their lines, Willian eventually put his boot through the ball to restore some parity.
From that point on it was one-way traffic for the majority of the first half, with Alonso testing Jordan Pickford with a stinger of a strike and Eden Hazard somehow failing to convert when picked out a few yards from goal.
Billy Jones produced a vital block to send Willian's curler narrowly wide of the far post as Chelsea pressed for a second, looking to pick up a 16th league win in 17 outings - Crystal Palace the only team to leave here with anything since September.
Sunderland had a big chance to restore their advantage right on the brink of half time, however, as from another free kick the ball this time fell to John O'Shea, who was the wrong man in the right place as he failed to beat Courtois.
A depleted Sunderland side, without 12 players this afternoon - leading scorer Jermain Defoe among them - were doing enough to keep their opponents at bay as the hour mark approached.
In the blink of an eye the champions were in front for the first time, though, after Diego Costa picked out Hazard to do the rest - the Belgian picking his spot from inside the box for goal number 16 of another impressive season.
Chelsea found themselves in complete control of the match without creating a great deal, until Pedro was gifted a goal soon after coming off the bench, nipping in to convert after Joleon Lescott headed a lofted ball past his own keeper.
There was still time left for Batshuayi to add a couple of goals, first getting on the end of Pedro's through-ball and slotting under Pickford, before cutting inside from the right and curling home a fifth of the afternoon for Chelsea with the final kick of the game.