Hazard’s spot-kick settled the west London derby, but Jose Mourinho’s side were made to work for the points after Charlie Austin’s 62nd-minute effort had cancelled out Oscar’s outstanding opening goal.
This was by no means the comfortable victory many had predicted for Chelsea against a side who started the day rooted in the bottom three.
But Chelsea’s power ultimately proved too much for Rangers, with Hazard’s pace and trickery allowing him to draw a foul from Eduardo Vargas before he dispatched the decisive penalty.
Harry Redknapp’s QPR received a timely boost at the start of the week when Austin’s double secured victory over Aston Villa to lift the Loftus Road club off the foot of the table.
That was only their second league win of the season, but Redknapp maintains that their performances have deserved more.
And the way the visitors started the first half suggested the manager’s insistence his players can drag themselves away from the relegation zone is not misplaced.
Chelsea’s outstanding form this season means Mourinho’s side are starting to acquire a fear factor.
But after surviving a lively opening, the visitors demonstrated their willingness to take the game to their hosts and created a number of openings that could have given them an unexpected lead.
As expected, Diego Costa returned to the Chelsea line-up after missing four matches with a combination of a virus and groin and hamstring injuries, and the Spain forward immediately made his presence felt.
Oscar drew a save from Rangers goalkeeper Rob Green and Branislav Ivanovic struck the side-netting with a near-post flick from Willian’s cross.
– Clever back-heel –
But Redknapp’s side were doing a good job of restricting Chelsea’s chances and posed their own threat when first Austin headed over and then when Leroy Fer led a breakaway, only to slip after wrong-footing two Chelsea defenders.
Mourinho’s side, though, have overpowered many of their opponents this season with the speed of their attacks, often instigated by Cesc Fabregas.
And the former Arsenal midfielder was the architect of the 32nd-minute move that led to Chelsea taking the lead.
Fabregas drove forward from midfield before picking out Oscar on the right-hand side of the box and the Brazil playmaker sumptuously curled the ball past Green from a tight angle with the outside of his right boot.
Rangers were understandably deflated and for a period at the start of the second half, Chelsea threatened to run riot.
Hazard narrowly failed to connect with Willian’s cross and the home side were convinced they should have had a penalty when Hazard went down after being pushed by Sandro.
But QPR refused to give in and they stunned the home side by drawing level when Austin cleverly diverted Fer’s volley past Thibaut Courtois with a back-heel. It was the 25-year-old’s fifth goal in nine league games.
Chelsea could have found themselves behind seven minutes later when Sandro’s shot drifted inches wide after being deflected off Fabregas’s boot.
Mourinho was growing more animated on the touchline as his side appeared to be in danger of running out of ideas.
But before the nerves could really set in for the home side, they were gifted the chance to reclaim the lead when Eduardo Vargas clumsily challenged Hazard on the left-hand edge of the Rangers area.
This time referee Mike Jones pointed to the spot and Hazard finished the job, converting confidently from 12 yards.