Chelsea took the lead when Hazard dived into James McArthur into the box to win a penalty, and then headed in his own missed attempt from the spot kick. In the second half, Jose Mourinho provoked the critics by immediately removing Cuadrado for the much more defensive John Obi Mikel, and Chelsea set about dominating possession but doing little with it.
Branislav Ivanovic went closest for Chelsea towards the end of the half, but Chelsea were happy to take the single-goal victory to seal the title.
16' - CUADRADO SHOT - Advancing on goal. Cuadrado slips as he fizzes a shot at goal from 30 yards, sending the ball just over.
24' - SPERONI SAVE - Speroni flaps at a corner, punches it into the air, and takes an age to drop to Matic, totally unmarked by everyone, but Speroni rushes back to block the shot.
27' - DROGBA FREE KICK - Drogba loops a well hit shot over the wall and Speroni tries to grab hold, dropping the ball. As defenders and strikers rush in, Speroni hooks the ball away.
44' - PENALTY! Hazard skips into the box, McArthur pulls away but can't do in time, with Hazard keen on hitting him in any event.
45'- GOAL! Chelsea 1-0 Palace. Hazard scores - It's a dreadful penalty, low and slow at Speroni, but the ball loops up and is headed in calmly by Hazard.
79' - IVANOVIC CHANCE - Willian clips in a wretched cross after a dreadful coupe of dummies from a free kick, the ball comes to Cahill and his shot is blocked, and then Ivanovic lashes over.
Chelsea have lost just one of their last 15 league matches against Crystal Palace (W10 D4 L1).
Alan Pardew has won four of his last seven Premier League matches as an opposition coach against Chelsea.
Chelsea have scored 199 goals in Premier League London derbies at Stamford Bridge.
Jose Mourinho has coached Chelsea in 96 Premier League games at Stamford Bridge, losing just one (W75 D20 L1)
The Blues have kept six clean sheets in their last seven Premier League games against London opposition.
The Blues have kept the most clean sheets in the Premier League this season (17), while Palace have kept the joint-fewest (6).
Their 2004-05 crown came in the 35th game, their 2005-06 one in the 36th game and their 2009-10 triumph on the final day.
Chelsea demonstrated half of what makes them worthy champions. The sheer concentration and control required to win a game 1-0 when it is tempting to go for the jugular requires mental strength that many other sides don't possess, as Chelsea's rivals demonstrate. But that ignores the occasionally astonishing attacking football of much of the season, and the relentless attacking talents of Eden Hazard over the course of the season. No other team came close.
MAN OF THE MATCH
Eden Hazard (Chelsea): If this game summed up Chelsea, this game summed up Hazard. Instrumental for Chelsea as they won, with an underrated degree of cynicism for such a supposedly (and probably genuinely) nice man of Hazard. It was an obvious dive, but without him Chelsea would have struggled this season.
Chelsea: Courtois 6, Ivanovic 6, Cahill 6, Terry 5, Azpilicueta 7, Cuadrado 6, Matic 6, Willian 6, Fabregas 6, Hazard 5, Drogba 6. Subs: Luis 6, Zouma 6, Mikel 6.
Crystal Palace: Speroni 5, Mariappa 6, Dann 6, Delaney 6, Ward 5, Ledley 5, McArthur 6, Puncheon 6, Mutch 5, Zaha 6, Bolasie 6. Subs: Kelly 6, Sanogo 6, Murray 6.