Robbie Brady curled in a low free-kick that caught out Boro keeper Jason Steele in the 62nd minute to give the Tigers all three points at the KC Stadium.
And Bruce admitted afterwards that the defeat to third-placed Watford on Tuesday had affected his team during the first half of Saturday's game.
"Tuesday was a huge disappointment to us all and I'm going to admit (on) Thursday and Friday they were still disappointed," said Bruce.
"It really took us to half-time to get going again, but we showed something, a bit of resilience and that determination to get a result. We don't want to be sitting through too many of them."
On match-winner Brady's fortunate strike, Bruce joked: "I've heard some nonsense that he watched somebody do it, whether it was (Cristiano) Ronaldo or (Gareth) Bale, and bounced it in front of the keeper. Looks to me like it hit a divot and the goalkeeper made a mess of it.
"But we needed a break and thankfully we've got it. It's put us in a really, really strong position, a good position and it's in our hands with five to play."