Arsenal cruised to an easy 3-0 victory over last-place Wolverhampton Wanderers on Wednesday to strengthen its grip on third place in the Premier League.
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.
In contrast, bottom side Wolves moved a step closer to relegation after a seventh successive defeat.
The two early goals and Bassong's departure effectively killed the game as a contest, although the home side could not be faulted for effort with Kevin Doyle impressing as the lone striker.
Arsenal's turnaround has been remarkable as they registered a ninth win in 10 games after trailing Spurs at the start of February by eight points.
Van Persie had the first attempt on goal after his own corner had been cleared straight back to him, but the striker's low volley was comfortably dealt with by Wolves goalkeeper Wayne Hennessey.
Matt Jarvis posed the first moment of danger to the Gunners but his probing centre just eluded Doyle at the far post.
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 sent off by referee Neil Swarbrick.
Van Persie stepped up and coolly dinked the ball over Hennessey after he had dived to the right for his 34th goal of the season and first in five matches.
Wolves made an instant substitution with centre-back Christophe Berra replacing midfielder David Davis as they reverted to a 4-4-1 system.
However, they 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.
In a rare Wolves attack Berra had a header deflected wide from a Michael Kightly corner.
Santos screwed a shot across the face of goal but the Gunners looked to have lost some of their early intensity, such was their control of the game.
Arsenal were soon back on the offensive in the second half and Aaron Ramsey had a shot blocked by Richard Stearman after a run into the box before Mikel Arteta teed up a good chance which Van Persie fired wide.
Wolves were showing plenty of fight and a superb save from Wojciech Szczesny denied Doyle.
Jarvis sent over a perfect cross for the Republic of Ireland international but his header was palmed away by Szczesny at full stretch.
However, Benayoun ended the mini revival by making it 3-0 after 68 minutes. Milijas lost the ball in midfield and Song teed up Benayoun 20 yards out to beat Hennessey with a low drive.
Doyle had a shot blocked by Johan Djourou as Wolves searched for a consolation goal.
Arsenal substitute Alex Oxlade-Chamberlain then had an effort from the edge of the box deflected past the post as his side ended the match on the offensive.
Wolves ended with a flourish as Szczesny turned aside a Milijas drive in injury-time, but they were well beaten.
