Brede Hangeland was dismissed for a two-footed first-half challenge on Lee Cattermole before second-half goals from Steven Fletcher, Carlos Cuellar and Stephane Sessegnon settled the contest.
"I'm delighted to win the game, sendings off change the dynamic of matches, we saw it in the Tottenham v Arsenal game," he said. "You have to try and take advantage of that and we did that in the second half.
"They were never out of the match but I was pleased for us to score some goals and win away from home, our goalkeeper has made two fantastic saves and he is having a fantastic season, and I thought Fletcher was fantastic too.
"Confidence is a big thing and when you see someone like Sessegnon score that type of goal, he has been searching for that confidence all season. His family have settled now which I think is important.
O'Neill was also happy to single out Adam Johnson for praise, adding: "Here he is having to start the matches, with respect to us we are not remotely as good as Manchester City.
"So he is having to strive, he is having to do more for us and he is getting there."