Oscar gave the Blues the lead in the first half, and though Charlie Austin threatened to claim a surprise point for the Rs, the Belgium winger stepped up from 12 yards to win it
Charlie Austin's second-half equaliser had looked set to deny Jose Mourinho's side a fifth consecutive league win at Stamford Bridge after Oscar had opened the scoring.
However, after Hazard was clumsily bundled over by Eduardo Vargas, the Belgian stroked home the winner to maintain Chelsea's four-point lead at the summit.
|By Wayne Veysey at Stamford Bridge
Chelsea were made to work hard for this narrow victory but have maintained their four-point lead over nearest challengers Southampton.
QPR were resilient and tenacious opponents, with Austin producing a fine piece of improvisation to equalise, but Chelsea had enough attacking stardust to wear them down eventually.
A fabulous Oscar strike set them on their way before Hazard won and then calmly converted the match-winning penalty.
With an under-par Chelsea on course to drop points for the second league game running, Vargas collided with Hazard just inside the area with referee Mike Jones pointing to the spot.
Hazard then had the final say 15 minutes from time as he tucked away the penalty to ensure Chelsea clinched maximum points and deny Harry Redknapp what would have been an impressive draw.
Chelsea began well and forced a series of corners early on, with leading scorer Diego Costa - back in the starting XI after a four-game absence due to a combination of injury and illness - almost getting on the end of Cesc Fabregas' long ball four minutes in.
Oscar saw a shot roll wide of Rob Green's left-hand post soon after before Branislav Ivanovic found the side-netting from Willian's delivery.
QPR – whose one change saw Junior Hoilett replace Bobby Zamora – produced their first effort on goal via the in-form Austin, whose header looped over the crossbar 15 minutes in.
While it was a rare foray into the Chelsea half, Redknapp's side had done well to stifle the hosts and initially deny the likes of Oscar, Willian and Hazard space to create openings.
However, after Fabregas' long-range strike tested Green from distance, Oscar opened the deadlock after 32 minutes courtesy of a sublime finish with the outside of the boot.
Played in down the right by Fabregas, the Brazil international found the bottom-left corner via the inside of the post to send Chelsea in ahead at the break.
Hazard almost doubled Chelsea's advantage early in the second half but failed to make contact with Willian's inviting cross as Redknapp opted to bring on Zamora for Hoilett just short of the hour mark.
Following a swift counter from Vargas, Austin was able to cleverly divert Leroy Fer's strike past a helpless Thibaut Courtois.
Mourinho then opted for an attacking change as Didier Drogba replaced Willian, but it was the ever-dangerous Hazard who was the match-winner.
Having been brought down by Vargas, the Belgium international sent Green the wrong way from the spot to get Chelsea back to winning ways in the league after their 1-1 draw at Old Trafford last time out.