Van Persie scored the opener from the penalty spot after Wolves' on-loan defender Sebastien Bassong was sent off for bringing down Walcott, who added a second a minute later. Yossi Benayoun netted the third after the break and the Gunners are now five points clear of fourth-placed Tottenham in the Barclays Premier League with just five games remaining.
After eight minutes Van Persie put Arsenal ahead from the penalty spot as Wolves were reduced to 10 men. Bassong was adjudged to have brought down Walcott as he raced onto Benayoun's pass and was dismissed.
Van Persie stepped up and coolly dinked the ball over Wayne Hennessey after he had dived to the right for his 34th goal of the season and first in five matches.
The hosts could not handle the pace of Walcott and he doubled Arsenal's lead after 10 minutes. The England player exchanged passes with Van Persie before curling the ball past Hennessey into the corner of the net.
Benayoun ended a mini Wolves revival by making it 3-0 after 68 minutes. Nenad Milijas lost the ball in midfield and Alex Song teed up Benayoun 20 yards out to beat Hennessey with a low drive.