The Holland international started the dreary midweek Champions League draw with Marseille on the bench, but was recalled to the starting line-up as Arsenal won their 400th Premier League game.
While unable to match his hat-trick heroics at Chelsea last weekend, Van Persie was the difference once more as he netted the first and then turned provider for both Thomas Vermaelen and Mikel Arteta.
Aaron Ramsey's exquisite through-ball helped the Arsenal skipper net his 11th league goal of the campaign, finishing from close range after Ben Foster blocked a Theo Walcott effort.
Vermaelen then netted his first goal for almost two years as he turned in a Van Persie cross and, after the break, Arteta fired home after neat work between the Dutchman and substitute Tomas Rosicky.
Van Persie and Laurent Koscielny were the only two changes Arsene Wenger made to his starting line-up heading into the match, while counterpart Roy Hodgson made four alterations to the side that lost 2-0 to Liverpool last weekend.
Arsenal started the stronger of the sides and dominated the early proceedings in north London, but were struggling to turn their possession into clear-cut chances.
Van Persie, fresh from collecting the October player of the month award, saw a shot blocked by Gareth McAuley inside the opening minute and then Andre Santos thumped a 20-yard free-kick over the bar.
Those attempts were all Arsenal had to show for their early exertions as the Baggies defended resolutely, with Jonas Olsson receiving a cut under his eye when challenging Vermaelen.
The patched-up Sweden international was forced to change shirt and shorts in order to continue for the visitors, who soon eked out their first opportunity as Simon Cox sent in a low cross that Zoltan Gera came close to pouncing on.
The Baggies were matching the home side with their endeavour, but were undone in the 22nd minute by an exquisite pass from Ramsey.
The Wales international's low ball cut through the West Brom defence and straight to Walcott, whose blocked shot fell kindly for Van Persie to net his 29th goal in 28 games this year.
The goal spurred Arsenal into life as they pressed for a second, with Arteta seeing a penalty shout rejected before Gervinho was adjudged offside in a dangerous position.
Wenger's side were still struggling to regularly test Ben Foster, but managed to double their advantage six minutes before the break.
Alex Song's ball to the back post was volleyed across goal by Van Persie, allowing Vermaelen to fire home his first of the season.
Arsenal continued to test West Brom's backline after the break and only a late block by McAuley stopped Carl Jenkinson's right-wing cross finding Gervinho.
Vermaelen headed just wide from the resulting corner as the home side pressed for a third, before Ramsey lashed across the face of goal.
West Brom were struggling to get out of their own half and only a quick reaction save from Foster thwarted a Song drive.
With less than 20 minutes remaining, Wenger brought on Yossi Benayoun and Rosicky in a bid to add another attacking dimension and force a third.
The move immediately had the desired effect as Arsenal scored with the next attack as Van Persie and Rosicky played a neat one-two, before the former teed up Arteta to fire home from 20 yards.
Somen Tchoyi saw a shot blocked by Vermaelen at the other end as West Brom looked to reduce the deficit, although Arsenal were still dominating the majority of possession.
Steven Reid tested Wojciech Szczesny with a late header, but the Gunners held out for a comfortable victory and a clean sheet.