The Tigers moved out of the relegation zone after goals from Gaston Ramirez, James Chester and Nikica Jelavic clinched a 3-1 triumph at the Stadium of Light.
It ended Hull’s long search for a first win since early October at the 11th attempt and set up nicely tomorrow’s visit to the KC of Nigel Pearson’s Foxes.
Bruce said: “Leicester is a huge game. We needed that victory and it gives us some confidence at the right time.
“I felt the best team won at a canter. Especially in the second half, I thought it was a total domination for us.
“But it will mean nothing if we don’t turn over Leicester. That is a huge game.
“If we can turn over them, it will be a big ask for them to catch us. So, that is what we have got to do.”
The win at Sunderland was only Hull’s third of the season and their first since beating Crystal Palace at the KC on October 4.
That triumph over the Eagles is the only time the Tigers have claimed maximum points from eight games on home soil.
Bruce added: “We have somehow got to take our away form, which has been decent, back home.
“Our home form was our biggest strength last season. Seven wins there made sure we stayed up.
“I am still convinced, from what I have seen, that if we turn our home form around then we will still be better off than last season.”
Hull’s fourth win over Sunderland under Bruce in as many attempts was not without controversy, the hosts having two penalty appeals for handball against Alex Bruce and Stephen Quinn turned down towards the end of the first half.
Asked if he felt referee Andre Marriner had got it wrong on both counts, Black Cats manager Gus Poyet replied: “You should not even ask me. If you say that, it is because you support Hull too much.”
Bruce, however, had a different take. The Tigers’ chief, who will be without Chester against the Foxes through suspension, said: “For me, the referee has got it right. They are a difficult one.
“Quinn’s, in particular, is when his hand is trying to protect his face. He does take it on the chin.
“When it is close to you like that, how are you supposed to get out of the way? For me, the referee showed common sense.
“I don’t see either being blatant, either one of them. We got the decisions, which over the last eight weeks hasn’t been the case.
“So, if we did get one go for us, we gratefully take it.”
Hull’s triumph came at the end of a week that saw Bruce’s assistant Steve Agnew leave for Middlesbrough and a fall-out with Paul McShane that saw the Irish defender banished to train with the Under-21s.
Following on from Hatem Ben Arfa’s departure, Agnew’s exit saw the rumour-mill crank into over-drive with regards tales of problems behind the scenes.
Bruce, however, has been quick to dispel those suggestions and instead point out that Agnew left with his blessing.
He said: “Let me put this straight. Steve Agnew came to see me last Friday (December 19) and said he’d had an unbelievable offer to go back there.
“I gave him the weekend to think about it. (Boro chairman) Steve Gibson obviously thinks a lot of him, like I do.
“I didn’t want it to happen, but, sometimes, you have to shake him by the hand and say ‘Well done, Steve, thanks for your help’. I even joked to him ‘Any chance of getting a contract like that for me?’
“The world we live in in football, how could I deny a top lad that chance? That’s the truth. I hear all these conspiracy theories, but he’s gone with my best wishes.”
Hull’s triumph at the Stadium of Light was the highlight of a mixed afternoon for Yorkshire’s clubs.
Middlesbrough and Sheffield Wednesday both won, as Rotherham United came from two goals down to draw 2-2 in a thrilling derby with Huddersfield Town. Leeds United, meanwhile, slumped to a poor 2-0 home defeat against Wigan Athletic.
In the bottom two divisions, Bradford City moved into the League One play-offs with victory at Fleetwood Town, but perhaps the most notable result in the Football League came at Bootham Crescent as York City avoided setting an unwanted club record.
Keith Lowe netted the only goal against Accrington Stanley to ensure the Minstermen claimed a first home win in 14 attempts – in the process avoiding matching the horror run of 1981-82.
Results and tables: Pages 4 & 5.