Boro claimed a battling win after Lukas Jutkiewicz slammed home the winner in the second half after a polished move.
They survived a number of close calls, including the post being rattled after 30 seconds, but ultimately got the precious win on a day when promotion rivals Crystal Palace, Hull and Leicester all dropped points.
Mowbray said: "There were some big, big fixtures in the Championship today so it was vitally important that we won the game.
"We were in this position last year but we drew too many games that cost us, but we have learned from that.
"Today was tough for us. Blackburn may have only won one game in 10 but they have a lot of quality players and they play good football.
"They made it difficult for us and created some good chances.
"So it may have been a close run thing but we deserved it. It was a fantastic effort by the team, they dug deep and got a very good goal then worked hard to hold on to it."