Bendtner broke the deadlock inside the opening five minutes, before Chris Brunt equalised with a free kick driven straight through a non-existent Arsenal wall.
Kolo Toure regained the Gunners' lead in the 38th minute with a header from Andrei Arshavin's excellent delivery, with Bendtner effectively ending the contest on the stroke of half time with his second, and Arsenal's third.
Arsene Wenger surprisingly partnered Arshavin and Bendtner in attack, with Robin van Persie confined to the bench, but his decision was vindicated as early as the fourth minute.
Bendtner cut inside Gianni Zuiverloon and slotted past Scott Carson to open the scoring after being afforded far too much space on the edge of the box.
The Baggies were not deterred and hit back after Luke Moore was hauled down by Johan Djourou, with Chris Brunt drilling the subsequent free-kick under a hapless Arsenal wall in the 11th minute.
Bendtner squandered a clear-cut chance to regain Arsenal's lead minutes later when the striker beat the home side's offside trap before blasting the ball over the bar.
