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.
Barclays Prem
1 Chelsea 83
2 Man City 70
3 Arsenal 67
4 Man Utd 65
5 Liverpool 61
6 Tottenham 58
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.
Manchester City may no longer be able to call themselves Premier League champions but at least the indignity of missing out on the top-four has almost certainly been avoided after Sergio Aguero inspired them to victory at Tottenham.
A poor 2015 has seen Manuel Pellegrini's side go from title challengers to facing the prospect of potentially missing out on Champions League football.
That disaster has been almost certainly averted, though, after continuing their fine form against Tottenham, with Aguero securing a 1-0 win just hours after City were dethroned as English champions.
Their fight to retain the title had realistically ended several weeks back but Chelsea's rubber-stamping meant a reaction was required at White Hart Lane, especially having lost their last four league games on the road.
DECEMBER 2015 - NEWCASTLE 2 CHELSEA 1
Newcastle striker Papiss Cisse came off the bench to condemn Barclays Premier League leaders Chelsea to a first defeat of the season.
The Senegal international struck with his sixth goal of the season four minutes after replacing Remy Cabella, and then added a second 12 minutes from time.
Magpies defender Steven Taylor was dismissed for a second bookable offence and substitute Didier Drogba headed Jose Mourinho's men back into the game with seven minutes remaining to spark a desperate, but ultimately fruitless, late flurry.
It was Chelsea's third successive league defeat on Tyneside and left Mourinho still awaiting his first win in the competition at St James' Park.
Even the returning Diego Costa could not prevent a Newcastle victory as rookie goalkeeper Jak Alnwick, who had replaced the injured Rob Elliot at the break, denied he and then defender Felipe Luis at the end in front of a crowd of 52,019.
Chelsea arrived on Tyneside defending a 21-game unbeaten run since the start of the season and they began in ominous fashion with Newcastle's policy of allowing opponents possession in front of them and attempting to hit them on the break resulting in one-way traffic for much of the opening half-hour.
With Costa restored to the side after suspension and Oscar, Eden Hazard and Cesc Fabregas buzzing about behind him, they were utterly dominant in the early stages.
After Willian had twice shot wide, Fabregas saw a 23rd-minute effort deflected past the post after Taylor had blocked Hazard's initial attempt, and Elliot had to save from Costa after Magpies midfielder Cheick Tiote had given the ball to Oscar.
But Newcastle finally found their feet and might have been ahead with 32 minutes gone when Thibaut Courtois blocked Jack Colback's shot with a foot.
As Moussa Sissoko started to drive the home side forward, the game opened up and Colback had to make a last-ditch challenge on Costa on halfway to deny the Spaniard a run on goal.
However, the visitors continued to threaten and Costa went just wide with an acrobatic overhead kick on the stroke of half-time.
Pardew was forced to make a change at the break when Elliot, deputising for the injured Tim Krul, failed to reappear and was replaced by 21-year-old Alnwick, making his senior debut for the club.
The newcomer's goal came under immediate threat with Paul Dummett and Taylor clearing low, driven Hazard crosses and Alnwick punching clear a Fabregas free-kick, flooring Costa in the process.
Pardew replaced midfielder Remy Cabella with Cisse eight minutes into the second half and the Magpies responded, although they were fortunate that John Obi Mikel powered a header wide from a Fabregas free-kick when he might have done better.
Newcastle took full advantage with 57 minutes gone when Gary Cahill failed to cut out Ameobi's left-wing cross and Cisse slid home from close range, his second goal in five days.
Sissoko could have doubled his side's advantage on the hour, but looped a header over after a Colback corner had been helped on at the near post.
Alnwick saved from substitute Andre Schurrle in the 62nd minute, before Mourinho sent on Luis and Drogba for Cesar Azpilicueta and Willian in a bid to inject fresh impetus into his team.
Chelsea hammered away at the Newcastle rearguard as it dropped ever deeper and Alnwick was grateful for the assistance of his left post to keep out Hazard's steered effort with 12 minutes remaining.
But their hopes of a comeback were dashed within seconds when the home side broke at pace for Sissoko to set up Cisse, who made no mistake.
Chelsea were given fresh hope with nine minutes remaining when Taylor, who had earlier been booked for a foul on Willian, lunged at Schurrle and was cautioned for a second time, and Drogba glanced the resulting free-kick past Alnwick to reduce the deficit.
But even with six minutes of stoppage time in which to find an equaliser, they were unable to deny the 10 men victory.