United captain Michael Doyle had earlier threatened to take the tie into extra time when he levelled from long-range but the Albion defender had other ideas.
Rowett said: "It goes without saying that I'm delighted to go through.
"Those were two great finishes from Chris but we also had to show the other side of our character at times because United are a good team.
"They put us under pressure for periods. But we dug in and took our chances when they arose.
"We always knew we'd have to work with and without the football. The lads did exactly what we asked of them and I can't praise them enough.
"The challenge now is to try and ensure we maintain the same standards. Especially in the league."
- Sports & Recreation
- Chris Hussey