Second-half goals from Olivier Giroud and Alexis Sanchez secured all three points for Arsene Wenger's side, although they were denied the chance to extend their gap over Manchester United when Louis van Gaal's side scored late on to beat Newcastle.
Charlie Austin wasted three clear chances in the opening 45 minutes for QPR as they restricted the visitors well with tight marking and a high tempo.
As a result, Arsenal initially offered little going forward, but after half-time words from Wenger, they finally found more in the second period.
Mesut Ozil wasted a fine chance before Giroud finally beat Rob Green from close range to open the scoring, and then Alexis sealed the win with 21 minutes left.
Austin got the goal his performance deserved with eight minutes remaining to give QPR brief hope, but it was in vain.
The result leaves QPR three points from safety, mired in the Premier League's relegation zone.
The hosts - who welcomed back Sandro for his first start since November - edged the opening exchanges, their high pressing game creating two chances for Austin that David Ospina saved easily.
Midway through the first half, Austin went up against Ospina once more, the striker again failing to stretch the Colombia international after Bobby Zamora had eased Gabriel Paulista off the ball.
That chance seemed to wake up Arsenal - who made two changes from their win over Everton - and within 60 seconds Giroud had their first effort on target, but his low shot was comfortably gathered by Green.
Austin's personal crusade to give QPR the lead continued seven minutes before the break, when he brought a loose ball under control before firing narrowly wide from 20 yards.
With half-time looming, Green was stretched for the first time following a crisp Arsenal move. Santi Cazorla exchanged passes with Giroud on the edge of the penalty area before volleying at goal, but Green pushed the ball away to safety.
Having failed to impress in the opening 45 minutes, Arsenal raced out of the blocks in the second period and they should have been ahead within two minutes of the restart, but Ozil was unable to convert Tomas Rosicky's cross.
Both sides wasted chances prior to the hour mark, before Arsenal finally broke the deadlock after 64 minutes through Giroud.
A swift break from Alexis created a crossing chance for Kieran Gibbs and when QPR failed to clear his ball into the box, France international Giroud scooped the ball home from close range.
The floodgates looked to have opened, and Arsenal punished their hosts further when Alexis converted five minutes later, beating Green low at his near post.
A superb save from Green denied Arsenal a third goal in quick succession as they looked to kill the game off - the goalkeeper making a fine stop from Alexis before QPR began to find their feet.
Austin gave them hope with an 82nd-minute strike when he finally beat Ospina after a neat turn on the edge of the penalty area, but it was not enough as Arsenal held on.
