Oscar tapped in the opener and added two fine finishes before Hazard converted a penalty for his first goal of the season.
Bertrand Traore, whose recruitment by Chelsea is under scrutiny, added a fifth after replacing Diego Costa, who posed for selfies and signed autographs as the game meandered to a conclusion.
Bradford came from 2-0 down to win 4-2 at Stamford Bridge in the fourth round last season but there was to be no repeat at stadium:mk, despite Chelsea's early profligacy and Darren Potter's deflected strike drawing MK Dons level at 1-1 for a short time.
The Blues soon found the net with ease and so did Hazard - for the first time since May 3, when Chelsea won the Premier League title against Crystal Palace.
It appeared that captain John Terry intervened to ensure Hazard, rather than Oscar, took the spot-kick and the Belgian sent David Martin the wrong way before celebrating in front of the visiting support by kissing the Chelsea badge.
Hazard has been linked with a move away from Stamford Bridge during a chaotic season, which saw him displaced as penalty-taker after misses earlier in the campaign.
Chelsea beat Arsenal last weekend and are now unbeaten in nine games since Jose Mourinho's departure, eight of them under Guus Hiddink.
MK Dons, who lost 3-1 at troubled Bolton last weekend and are fighting to retain their second-tier status, never really tested the Blues, who found holes aplenty to exploit.
Costa had six goals in six games entering the contest and should have enhanced his scoring streak in the opening moments, but Martin saved his lazy shot from point-blank range.
Branislav Ivanovic was denied on the turn before a woeful intended back-pass from Kyle McFadzean was seized upon by Costa, who centred for Oscar to slide the ball in.
MK Dons had a few forays forward and Samir Carruthers' shot was gathered at second attempt by Thibaut Courtois before Potter's shot soared in off Nemanja Matic.
Hazard should have restored Chelsea's advantage when racing through on his first start in four weeks following a groin problem.
But the Belgian's confidence had eroded since his most recent goal - a headed rebound following his missed penalty in the title-winning game with Palace - and his shot was deflected by Martin on to the post
The goalkeeper gathered the rebound.
Chelsea soon had another chance when Baba Rahman slid the ball across, but Costa nipped in front of Oscar to divert the ball wide.
Costa smiled ruefully and Oscar soon had his second when he shot across the goalkeeper after being played in by Ruben Loftus-Cheek.
Oscar shot narrowly wide before being afforded the freedom of Milton Keynes to complete his hat-trick.
The Brazil playmaker cut in from the left, waltzed past three defenders and beat two more with a shot which Martin could do nothing about.
Unlike against Bradford, there was no reason for Chelsea to fear a fightback and Chelsea's three-goal lead was restored when Potter nudged Hazard over for a soft penalty.
The playmaker converted himself before turning provider, cutting the ball back for Traore to tuck the ball in.
Source : PA