The Black Cats are still some way off safety, but a Djibril Cisse strike was enough to see them leapfrog the Tigers and Blackburn Rovers in the league table.
The home side's display was not one for the faint-hearted with Ricky Sbragia's men defending for their lives at times.
However, in the end they stood firm and the final whistle was greeted by a mixture of ecstatic cheering and massive sighs of relief among the red and white faithful.
Before that the hosts had to endure some very nervy moments as Hull battled to try and take something from the clash. In the end though they were unable to find the breakthrough they craved.
That was largely due to a lack of shooting prowess in front of goal. City worked hard and forced the home side onto the back foot for long spells, but they never really tested Craig Gordon in the Sunderland goal.
The only time the Scot was called upon to make a save came in the 26th minute when ex-Sunderland player Kevin Kilbane headed at goal. Gordon got down to make the save and, apart from a few second-half punched clearances, was largely untried.
To be fair neither side was really able to grab the game by the scruff of the neck in the first half which was a fairly nervy and turgid encounter.
The Tigers seemed to be relying on the high ball over the top and, while that had the Black Cats at sixes and sevens from time to time, it never paid off as far as goals were concerned.
Sbragia had said before the game that his side would favour the direct approach but there was little evidence of that in the opening stages.
In fact it was City who were asking most of the questions in the first half, but it was the hosts who had the final say.
With half-time looming, Cisse swooped with a header to put his side in front against the run of play. Andy Reid's cross was flicked on by Danny Collins and Cisse stooped to guide the ball into the Hull net.
It had taken almost all of the first half for the Wearsiders to really get going, but they were quickest out of the blocks after the break.
Buoyed by Cisse's finish, the Black Cats went after the Tigers at the start of the second half but they couldn't convert their attacking impetus into further goals.
As the game wore on you could sense a feeling of nervousness wash over the Stadium of Light both on and off the field.
The home team defended deeply and time and time again were forced to hack the ball clear under pressure.
Hull pressed and went close through George Boateng, who fired just wide from 25 yards out before substitute Caleb Folan headed narrowly off target from Sam Ricketts' cross.
Those missed chances just about summed up a frustrating afternoon for City whose alarming slide towards the relegation zone shows no sign of stopping.
The Black Cats almost heaped more misery on the visitors as Daryl Murphy's late strike rocketed off the inside of the far post.
It was not to be, but that won't worry the Wearsiders who gave themselves some respite from the relegation battle thanks to the three precious points.