The Dane netted on his first start for almost three years to give the Gunners a second-minute lead before the 40 million man ensured they remain clear at the top.
Bendtner's inclusion in the Arsenal XI raised eyebrows, but the Dane answered his critics in the perfect fashion, thundering a header home from Carl Jenkinson's cross in just the second minute after superb interplay from Tomas Rosicky and Aaron Ramsey.
Mesut Ozil doubled the home side's advantage two minutes into the second half as Arsene Wenger's side eased to victory at the Emirates Stadium.
Hull never looked likely to recreate its heroics from Sunday's win over Liverpool as Arsenal maintained a four-point advantage at the top of the Premier League.
Bendtner came in as one of five Arsenal changes from the weekend win over Cardiff City, while Hull boss Steve Bruce made two alterations to the side that beat Liverpool - the suspended Curtis Davies replaced by James Chester in defence and Danny Graham coming in for Robert Koren.
Arsenal made the perfect start as Bendtner rose highest to plant Jenkinson's fine cross home after typically intricate build-up play.
The Dane could have doubled his tally 14 minutes in, but a heavy touch spoiled his chances after Allan McGregor had spilled Ozil's drive.
Arsenal was irrepressible, but Ramsey and Laurent Koscielny hit efforts over the crossbar, while McGregor dived to his left to keep a 25-yarder from the Welshman out.
Hull grew into the half as it wore on, Tom Huddlestone flashing a ball across the six-yard box and Chester heading wide from a corner as the teams went into halftime a goal behind.
But Arsenal started the second half just as well as the first, Ozil playing a sharp one-two with Ramsey down the left channel before slotting past McGregor at his near post.
Ramsey then forced a smart stop from McGregor from a narrow angle with Robbie Brady having to head Bendtner's header from the resulting corner off the line.
Arsenal pressed on and Santi Cazorla went close on the hour mark, jinking past three players inside the area before seeing his fierce left-footed shot deflected wide by Chester.
Bendtner was afforded a standing ovation in the 72nd minute as he was replaced by Theo Walcott, rounding off a hugely positive outing for the much-maligned striker.
Ozil was denied a second by a desperate block from Hull substitute Liam Rosenior, while faint home appeals for a penalty were waved away as Jack Wilshere tumbled in the box under Chester's challenge.
But Wenger's side comfortably saw out the remainder, securing a fourth consecutive 2-0 victory on home soil.