Bendtner - whose last Arsenal run-out had come in August 2011, since when he had been loaned to Sunderland and Juventus and then failed to secure another move over the summer - spearheaded the attack in a first XI showing nine changes from Sunday's Barclays Premier League win over Stoke.
The 25-year-old Denmark international had an unfortunate collision with a post early on but made a better impact in the 61st minute, playing a through ball for Thomas Eisfeld, who latched on to it and slotted in the opening goal.
Saido Berahino headed an equaliser 10 minutes later and the score remained 1-1 after extra time, in which Bendtner had the ball taken away from him by a superb Craig Dawson tackle when he was through on goal.
Bendtner then converted in the shoot-out, won 4-3 by the visitors thanks to Nacho Monreal's decisive penalty following missed ones from Dawson and Albion substitute Morgan Amalfitano, who had sent a shot against the bar in extra time.
Asked about Bendtner after the third-round tie, Wenger said: "I thought overall he had a good game.
"For a guy who has not played for such a long time, and on his own up front, he did very well.'"
On the incident where Bendtner was tackled by Dawson, Wenger said: "What happened to him is what happens to many strikers when they have too much time to score - they wait and wait, and wait for too long. But overall, I thought his game was positive.
"One thing you don't question too much with him is his confidence.
"I believe for Nicklas, the most important thing for him is to stay fit. As for the rest, he has the talent.
"It is important that he is now consistently present and works hard physically. He has top qualities."
Wenger fielded several young players inexperienced at this level, such as 20-year-old first-time starter Eisfeld, debutant Isaac Hayden, Kris Olsson - another making his senior bow - and Chuba Akpom, with the latter pair coming off the bench and scoring in the shoot-out.
Wenger, whose team host Chelsea in round four, said: "I am proud. We played with many young players and they showed they are not only good footballers but that they can fight as well.
"I decided to go for young players with the penalties and they coped well with the pressure."
West Brom made eight changes to their starting line-up from their Premier League win over Sunderland and Albion joint-assistant head coach Kevin Keen felt the team had performed well.
"I think over the 90 minutes we probably just about shaded it and over the 120 we definitely shaded it," Keen said.
"So to come away without going through to the next round is rather deflating - and the lads are disappointed."
- Sports & Recreation
- Barclays Premier League
- Thomas Eisfeld
- Craig Dawson