Boro bounced back from consecutive defeats to Cardiff and Bristol City with a Scott McDonald double either side of Emmanuel Ledesma's free-kick.
The win moved the Teessiders back up to third and closed on top two Cardiff and Crystal Palace, who were both held to draws.
"Any win's a good win in this league - it's a very hard league," said Mowbray. "It was important to get back to winning ways and I think they showed tonight that confidence hasn't been dented.
"I think with the weekend (defeat to Bristol City), the potential was there to knock the confidence and the belief.
"Yet the team showed a real resilience tonight to match a very hard-working team. We managed to get the points and we'll put them in the bag and move on to the next game.
While McDonald caught the eye with his two-goal cameo, his manager was quick to point to his other qualities.
"He's come back into the fray the last couple of months and he's done exceptionally well for us. I think what he brings as well as his goals is his work ethic from the front," said Mowbray.
"People can talk about the goals and think 'he must have played well' and yet the coach's eye and hopefully the player's eye sees the unselfish work that Scott does for the team."