The 24-year-old scored the quickest goal of the Premier League season after just 20 seconds as the Gunners jumped above Tottenham and Chelsea.
The victory sees the Gunners maintain the pressure on both Chelsea and Tottenham as they moved above the pair into the final automatic spot for Champions League football.
Harry Redknapp made four changes to side condemned to Championship football last Sunday, as Jose Bosingwa, Adel Taarabt, Esteban Granero and Jay Bothroyd made way for Tal Ben-Haim, Andros Townsend, Ji-Sung Park and Bobby Zamora.
There was just one change for Arsenal, as Nacho Monreal started in place of the injured Kieran Gibbs.
The north London side made the perfect start when it was given a helping hand by one of the club's old boys, as Armand Traore misplaced a header to allow Tomas Rosicky to gain possession and find Walcott to slide past Robert Green for the opener.
Walcott nearly doubled his tally soon after with Rosicky cutting in from the left side and again finding the winger, but his effort was flicked onto the post by Green.
QPR was struggling to cope with the pace of Asenal but Andros Townsend was the team's brightest spark throughout, with his first real involvement allowing Bobby Zamora to find Ji-Sung Park, but the South Korean could only blaze his effort over the bar.
Despite the bright opening, the Gunners struggled to build on their advantage by wasting a number of good opportunities and went into the break with just a one-goal lead.
QPR looked far more assertive in the second half with substitute Shaun Derry and Townsend both lively against a stern opposition defense, with the latter stinging Wojciech Szczesny's palms before Remy went close moments later.
Seemingly sensing an equalizer, the QPR started to press forward more with Santi Cazorla trying his luck from 25 yards but again Green was more than a match to the shot.
Townsend went closest for the Rs with five minutes remaining, cutting inside and curling a shot towards the far post, only for Szczesny to force the ball away with a strong hand.