The Gunners captain had 90 minutes to net twice against the R's to equal Alan Shearer's record of Premier League goals in a calendar year.
Having wasted four decent chances in the first period, van Persie swept home his first opportunity of the second half after latching onto Andrey Arshavin's neat ball.
However, the Holland international failed to add to his 60th minute effort and missed the chance to equal the former Blackburn striker's 36-goal haul from 1995.
Van Persie was not the only Arsenal player left ruing missed opportunities, with Theo Walcott and substitute Gervinho both guilty of failing to convert gilt-edged chances.
The Gunners' futility led to a nervy ending against spirited QPR, although resolute defending saw the majority of the 60,067 crowd go home happy.
Before kick-off Arsenal legend Tony Adams was given a standing ovation on the Emirates pitch.
The former captain's appearance failed to boost today's side, though, with QPR dominating the opening exchanges.
After Per Mertesacker thwarted an Adel Taarabt through ball, ex-Arsenal striker Jay Bothroyd soon found space to get away a 20-yard effort on goal in the ninth minute.
Wojciech Szczesny held with ease but looked less comfortable when an exquisite Taarabt pass put Shaun Wright-Phillips behind the Gunners' backline a minute later, forcing the Polish goalkeeper into a quick block.
QPR were playing with confidence in north London, although a moment of van Persie magic could have easily seen the home side break the deadlock.
The Arsenal skipper jinked back and forth on the right-hand side, before sneaking past his marker and toe-poking an effort on goal from close range, but without success.
Former Tottenham playmaker Taarabt was fortunate to escape punishment from referee Martin Atkinson in the 19th minute when he seemingly caught Arshavin with a stray arm.
Joey Barton fired a shot across the face of goal with the Russia international still grounded, before van Persie twice came close at the other end.
The Dutch striker first backtracked furiously to head just wide, before wriggling past Luke Young in the box and lifting the ball just over the bar.
The Gunners were in the ascendancy and van Persie fired just over the bar after being put through by a long ball from the back.
Arsenal twice had penalty shouts rejected as half-time approached, before a goalbound Aaron Ramsey effort was cleared off the line by Barton and Cerny parried a fierce Mikel Arteta drive.
QPR looked rejuvenated after the break and Jamie Mackie found the net within two minutes, although the whistle had already been blown for offside.
Armand Traore's dangerous left-wing cross caught Arsenal off guard five minutes later, but Alejandro Faurlin's miscued shot allowed Szczesny to gather comfortably.
Wenger's side were looking most dangerous on the break and Walcott should have scored the afternoon's opening goal in the 56th minute.
Ramsey put the former Southampton man through one on one with Cerny and, despite the goalkeeper diving the wrong way, Walcott somehow pulled his shot wide.
Fortunately that lack of composure did not haunt the Gunners, who broke the deadlock through van Persie four minutes later.
Arshavin found time and space on the left flank to find the Arsenal skipper, who swept a left-footed drive past Cerny inside the box.
Young's block stopped Arshavin doubling the north Londoners' advantage, before Taarabt forced Szczesny into a low save to prevent a curling effort finding the net.
The shot began a bright spell for the west Londoners, who saw Connolly blaze over and felt aggrieved not to receive a penalty when Taarabt went down under substitute Francis Coquelin's challenge.
Arsenal, having seen a rasping Ramsey effort come close, were close again through Gervinho.
The indomitable van Persie showed strength and skill to lose his marker and cross for the Ivory Coast international, who somehow put wide from close range.
Arsenal continued to press for a second as the game drew to a close but were thwarted, with Ramsey and van Persie both unable to find the net.