The 25-year-old was recalled to the starting XI to give leading forward Olivier Giroud a rest, and headed the hosts in front inside two minutes.
Mesut Ozil extended Arsenal's lead at the start of the second half, finishing off a fine passing exchange with Aaron Ramsey.
Bendtner's last league start for Arsenal came three seasons ago and he almost left the club in the summer following several unsuccessful loan spells and hitting the headlines with his off-field behaviour.
Wenger, though, feels the 6ft 3in forward has the attributes to produce consistent performances if he is fully focused.
"Look, [it is a gamble] if a guy has not played for a long time, and his last performance was not convincing against Chelsea, but he has worked hard in training and deserved a chance," said Wenger.
"We know that when he has the mind on the game, he has the qualities. I believe tonight he had a good game.
"He has the stature, he has good technical quality, he has quite good pace.
"We had him as a boy of 15 or 16 and I made him sign a long contract twice, so that means I always believed in his qualities."
Wenger had made several changes from the team which won at Cardiff including starting with England trio Jack Wilshere, Theo Walcott and Kieran Gibbs on the bench.
"We had a good night because we had a good control of the game. We had some great technical quality and keep a clean sheet," he said.
"We couldn't take all the chances we created, but overall it was a very convincing performance."
The Gunners' victory saw them maintain a four-point lead over second-placed Chelsea, who won 4-3 at relegation battlers Sunderland, and moved further ahead of Manchester United, who lost at home to Everton.
Wenger, though, will not rule the champions out of the title race just yet.
"It is a surprising defeat [to Everton], but it is still early," Wenger said.
"We have seen that before, 12 points, only on us.
"We have just to keep winning to have a chance, and not worry too much about the others."
Arsenal host Everton on Sunday, then travel to Napoli for their final Champions League group match before a crunch clash at Manchester City on Saturday lunchtime.
Wenger said: "We have a very heavy schedule, that's why as well I had to rest some players today and to rotate.
"There is little distance between Everton and [the Napoli game]. We play Wednesday night in Naples and Saturday morning at Man City, so for us it is a very, very heavy schedule."
Wenger continued: "It is not fair or unfair, it is just no co-ordination between the television choices because you would say that we could have played on Saturday against Everton and we could play Sunday or Monday against Man City.
"It looks strange that we play Saturday morning and our next game after that is Monday night against Chelsea nine days later.
"Especially when there is little time between a decisive Champions League game on Wednesday night and Saturday 12.45pm."
Hull boss Steve Bruce, who was involved in an exchange with some Arsenal supporters behind the dugout during the closing stages, was Bendtner's manager when the striker was on a loan spell at Birmingham and then at Sunderland.
"He is a good football player for the size of him. I hope that sooner or later he really knuckles down and really makes a go of his career because he's a very, very good player, but the mentality of Nicklas is always what everybody questions," said Bruce.
"He's a big, strong, powerful centre-forward who's good in the air and has good feet for the size of him. He's got the lot really, if he wants it - but there's always a 'but'."
Bruce added: "Did we try to sign him in the summer? We were having a look, but the level of salary was always going to be a problem for us.
"Nicklas is a good boy, he has always done well for me and it was Sod's Law he would do that against us today.
"When was the last time he scored? It was for me (at Sunderland) wasn't it? Well, there you go."