Robert Snodgrass scored the only goal of the match 15 minutes to full-time to ensure three points for the home team.
The strike was assisted by the season’s talisman Albert Adomah, who himself, was a major doubt for the game following his injury withdrawal from Tuesday's defeat to Brentford after just 18 minutes.
"We've had three centre forwards missing tonight, two central midfielders, two centre-backs and two full-backs," Bruce said, as reported by his club's official website.
"And we've come up to Middlesbrough and played very well. I'm delighted.
"I hope it shuts a few people up again. It becomes very annoying being a week away from a crisis.
"We've got to stop that and get on with the job in hand – to try and take the club forward again."
Villa had to do without the likes of Glenn Whelan, Keinan Davies, Jonathan Kodjia, John Terry and Gabriel Agbonlahor.
"That's not easy," said, Bruce.
"Middlesbrough are a very good side, who've had a new manager come in and won three on the bounce.
"They've got some really good players all over the pitch, are physically big and they ask you questions.
"We stood up to that today and played very well. That little bit of quality from Adomah and Snodgrass has got us the winner."
Villa sit seventh on the table ahead of Monday's clash with Bristol City.