After a run of four successive goalless draws in the Premier League, Arsenal had this game sewn up before half-time.
Bendtner opened the scoring then helped himself to the third to take his tally for the season to 11 and was only denied a hat-trick when he hit the post in the 57th minute.
Albion had given themselves false hope when Chris Brunt quickly put them on level terms after Bendtner's early opener, but once Arsenal captain Kolo Toure regained the lead for the Gunners the result was a formality.
Arsenal are now three points behind fourth placed Aston Villa while Albion are still four points adrift of safety after crashing to a fourth successive defeat.
Having gone four games without a goal, Arsenal needed just four minutes to end that run - but it only took Albion another three to breach the Gunners defence for the first time in five matches and briefly raise their hopes of pulling off an unlikely upset.
Albion paid the price for failing to deal with a Samir Nasri corner.
Jonathan Greening's headed clearance flew straight to Denilson, who picked out Bendtner on the left hand edge of the area.
There initially appeared to be little danger but Bendtner easily cut inside Ryan Donk and beat Scott Carson with an angled drive.
It was just the start that Albion didn't want but their response was swift, although Arsenal's Emmanuel Eboue will know he could have done more to keep out Brunt's free-kick.
After Luke Moore had been fouled 25 yards out by Johan Djourou, Brunt let fly with a low drive that went straight through the legs of Eboue before beating Manuel Almunia just inside his near post.
While Bendtner could have regained the initiative for Arsenal in the 13th minute when he blazed a pass from Eboue over the bar, Brunt's equaliser had galvanized Albion and they were fortunate not to take the lead themselves just 60 seconds later.
Moore got clear in the box and let fly with a vicious low drive that Almunia did well to hold at the foot of the post.
Moore, who was only in the starting line-up because Albion could not play on-loan Arsenal striker Jay Simpson, was making himself a nuisance in the opposition area.
He was again close to scoring in the 36th minute when his header flew just over the bar after Abdoulaye Meite had headed back Brunt's corner.
It was a turning point as Arsenal were in the ascendancy again two minutes later when Albion were again undone by their failure to defend set-pieces.
Toure was able to rise unchallenged to meet Andrey Arshavin's left-wing free-kick and buried his header past Carson from just six yards.
That was effectively game over and the result was put beyond any doubt a minute before half-time when Toure turned provider.
His long ball from inside the Arsenal half cut the Albion defence in half and Bendtner made light of the challenge from Meite to once again fire an angled drive beyond Carson from the left-hand side of the area.
All that was missing from Arsenal's performance was a first goal for Arshavin following his £15million arrival from Zenit St Petersburg.
He did his best to open his account, being denied by Carson in the 53rd minute and then shooting just wide seconds later.
There was no way back for outclassed Albion although they could have made the final 15 minutes interesting had Marc-Antoine Fortune's shot not whistled just inches the wrong side of the post.