Justin Hoyte's opener was cancelled out by a goal from Wednesday striker Gary Madine but further strikes from Ishmael Miller and substitute Lukas Jutkiewicz secured the points for the home side.
Boro chairman Steve Gibson halved ticket prices for the match and the move was rewarded as 28,229 supporters came to the Riverside Stadium.
"It was great to have such a big crowd there for us. A big thank you to all the supporters who came tonight, and thanks to the chairman who put the deal together," said Mowbray.
"That's what I know the Riverside as. We had 11 years in the Premier League with the stadium full. It's a 35,000-seater stadium and we've had 13, 14 and 15,000 this season and that's woefully empty.
"We're very appreciative of the people who've come along and spent their hard-earned money in the support of our club.
"The atmosphere of an exciting game is what the supporters want to feel, and thankfully we got the right result."
As for the game itself, the boss was understandably delighted with his side's performance.
"We're delighted with the points," added Mowbray. "Every game in this league is very, very tough, whether you're playing a team from the top or from the bottom.
"They've all got attributes that can hurt you and ultimately we got the three points tonight, even if we made hard work of it."