Jose Mourinho’s side needed three points to claim the trophy with three games to spare and Eden Hazard headed in the rebound after missing a first-half penalty.
Mourinho’s 21st trophy of his prolific career was the Capital One Cup win at Wembley in March – the first of his second spell at Stamford Bridge – and now the Portuguese has a third Premier League title and Chelsea’s fourth in 11 seasons.
The self-proclaimed Special One delivered the first title 10 years ago – the 2004-05 win was Chelsea’s first championship in 50 years – but domestic league success has eluded the Blues since Carlo Ancelotti led them to the 2009-10 title.
Chelsea entered Sunday’s fixtures 13 points clear of Manchester City and Arsenal, the only team who could overhaul them as they have a game in hand.
It was a nervous opening for the champions-elect, with Palace determined to prolong Chelsea’s wait for the title, roared on by a raucous visiting support which only served to remind Mourinho of his unhappiness at the home faithful this term.
Hazard has so often been Chelsea’s saviour and once again provided the spark which led to Chelsea’s penalty, although there was debate about the extent of the contact.
The Belgian’s spot-kick was saved by Julian Speroni, but he headed in the rebound to settle nerves with his 19th of the season.
Mourinho reaffirmed his “more strategic, less artistic” approach of recent weeks by sending on John Obi Mikel at half-time and Kurt Zouma late on.
Some have labelled it “boring”, but Chelsea and Mourinho cared not a jot as the Blues saw out victory and jubilant celebrations began.
Mourinho declared Chelsea’s title challenge over last season following a defeat at Selhurst Park and he was taking nothing for granted until the title was mathematically secure.
The Blues boss recalled Thibaut Courtois in goal, with Petr Cech dropping to the substitutes’ bench, and was forced into a late change when Ramires fell ill.
Juan Cuadrado came in against a Palace team showing four changes following the loss to Hull and determined to delay Chelsea’s coronation.
The pace was frenetic in the opening period, but there were few moments of quality and precious few attempts on goal.
Didier Drogba, up front again in the continued absence of Diego Costa, stung the palms of Speroni with a wickedly dipping free-kick after Cesc Fabregas had been fouled by Jason Puncheon.
Speroni scrambled clear under pressure from John Terry, who was then forced to throw his body down to deny Puncheon.
The Chelsea captain had deflected the ball into the path of the Palace playmaker, whose shot veered off Cesar Azpilicueta and hit Terry’s shoulder and upper arm before going clear.
Terry was booked – just his second caution of the season – for a foul on James McArthur as Chelsea continued to struggle to get a grip of the contest.
So often this year the Blues have looked to Hazard for inspiration and incision.
The Belgium playmaker provided it when he exchanged passes with Willian before being sandwiched by McArthur and Adrian Mariappa to earn a penalty.
Replays suggested the Professional Footballers’ Association Player of the Year, lauded for his attitude despite being the most fouled player in the league this season, may have gone down too easily.
Perhaps showing signs of nerves with his first Premier League title at stake, Hazard scuffed the resulting spot-kick.
Speroni saved, only for the Chelsea forward to send the goalkeeper the wrong way with a header from the rebound.
Mikel is usually sent on to close a game out and the Nigeria midfielder replaced the ineffective Cuadrado at the interval.
Chelsea kept possession, biding their time, with Branislav Ivanovic blasting wide from distance and Mikel engineered a chance after a one-two with Drogba, only for Speroni to save.
Palace continued to search for openings, but the last pass was frequently out of reach, such as when Wilfried Zaha tried to feed substitute Yaya Sanogo.
As Palace probed forwards, Chelsea continued to search for a second.
Ivanovic blasted over and Willian manufactured a chance for Drogba, but he could only fire into his standing foot and the ball spun wide.
Courtois saved from Zaha and Willian shot wide across goal on the counter-attack before making way for Kurt Zouma in another defensive change.
Palace fans responded by reprising the Arsenal chant from a week ago “boring, boring Chelsea”.
Still Palace tried to upset their hosts, but the Blues held on.
Mourinho celebrated with his family behind the dugout at the final whistle as the ticker tape fell and the players soaked up the acclaim.