The in-form Dutchman fired the Londoners into the lead from close range in the first half before Thomas Vermaelen doubled the Gunners’ advantage shortly after with a well-struck effort.
Mikel Arteta then made the points secure 15 minutes from time to give Arsenal their fourth straight league win and keep them in seventh place in the table, level with Liverpool on 19 points.
Despite enjoying almost three-quarters of the possession during the opening exchanges, Arsenal failed to conjure up any real opportunities of note until the 22nd minute.
Aaron Ramsey slotted a sublime defence-splitting pass through to Theo Walcott, and the England forward’s first-time shot was spilled by Ben Foster into the the path of Van Persie, who smashed home his 11th league goal of the season from the rebound to put the Gunners ahead.
The visitors never really troubled the Arsenal rearguard before the break – their only threatening moment came when Jerome Thomas had his appeals for a penalty waved away by referee Michael Oliver when he went down under a challenge by Laurent Koscielny.
And moments later, Vermaelen extended the Gunners’ lead. Van Persie volleyed an inviting pass across goal from the right and the the Belgian centre-half lashed in his shot from just inside the box.
Arsenal created the first chance of the second period when Alex Song’s first-time shot was punched away by Foster in the West Brom goal after 66 minutes.
And Arteta made the points secure eight minutes later. Van Persie exchanged passes with substitute Tomas Rosicky on the right and the Dutchman teed up the Spaniard, who coolly slotted his shot into the bottom-left corner from the edge of the box.
Arsenal: Wojciech Szczesny, AndrÃ© Santos, Thomas Vermaelen, Laurent Koscielny, Carl Jenkinson, Mikel Arteta, Alexandre Song, Theo Walcott (Andrey Arshavin, 78), Aaron Ramsey (Tomas Rosicky, 71), Robin van Persie, Gervinho (Yossi Benayoun, 72).
West Bromwich Albion: Ben Foster, Gareth McAuley, Jonas Olsson, Billy Jones, Graham Dorrans (George Thorne, 81), James Morrison, Steven Reid, Chris Brunt, Jerome Thomas, ZoltÃ¡n Gera (Somen Tchoyi, 63), Simon Cox (Youssuf Mulumbu, 71).
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