The result coupled with West Ham's win over Wigan means the Tigers are six points from safety with two games left and with a vastly inferior goal difference.
It could have been different had Jimmy Bullard scored a 41st-minute penalty rather than hit a post, while both sides were reduced to 10 men in first-half injury-time after an off-the-ball clash between Jozy Altidore and Alan Hutton.
Hull boss Iain Dowie said before the match he would make changes and he was as good as his word, bringing creativity into the side in the form of Geovanni and Nick Barmby and reverting to 4-4-2 with Altidore and Caleb Folan up front.
But Hull again made a woeful start and they could have been a goal down inside three minutes when Steed Malbranque found space inside the area. He teed up Jordan Henderson but the youngster made a mess of his side-footed effort from 10 yards.
Dowie must have been hoping the return of Anthony Gardner would shore up a leaky defence but moments later Malbranque was in again. This time he took the shot himself from a similar distance but it was well over the bar.
Hull could have had no complaints, though, when the visitors did take the lead in the seventh minute. A cross from right-back Hutton was headed across goal by Kenwyne Jones for Bent to tap in his 25th goal of the season from a tight angle.
The hosts at last strung a move together in the 19th minute but Barmby's cross was deflected behind and Folan could not get the ball out of his feet when the corner fell to him at the far post.
Missed chances have hurt Hull all season and they should have been level in the 26th minute when Bullard's corner landed on the head of Gardner six yards out but his effort hit the chest of Gordon and was cleared away.
It was a much more even game now and another searching Bullard cross picked out Barmby for a header over the bar, then in the 36th minute the hosts had another great opening when Altidore played Folan through.
He chose to shoot early as Hutton came in with a challenge and Gordon did well to tip the shot behind for a corner.
Folan was then involved in the incident that should have seen the Tigers draw level in the 41st minute. The striker looked slightly fortunate to get away with what appeared a tug on Hutton but the ball fell to Geovanni and he was sent tumbling in the area by Hull old boy Michael Turner.
Bullard is usually a confident penalty taker but he did not hit the ball cleanly and it rebounded to safety off Gordon's right-hand post.
With the referee about to blow the whistle for half-time, both sides were dramatically reduced to 10 men. Altidore and Hutton challenged for the ball near the byline, with the Sunderland defender then foolishly throwing the ball at the head of his opponent.
Altidore responded by headbutting Hutton, earning an immediate red card. With Sunderland boss Steve Bruce making his displeasure known at the Hull striker's challenge, referee Lee Probert waited for Hutton to receive treatment before, somewhat harshly, also giving the Scot his marching orders.
Both managers made changes for the second half, with Phil Bardsley and Anton Ferdinand coming on for Turner and Malbranque for Sunderland, while Cairney replaced Bullard for the hosts.
A foul on Cairney 25 yards out presented Geovanni with a decent opportunity but he could only strike his free-kick into the middle of the wall.
Hull were grateful to Duke for keeping them in the game in the 67th minute, the keeper tipping away Cana's 25-yard effort.
The Tigers were struggling to create chances but they came close to levelling in bizarre fashion in the 72nd minute. Andy Dawson's shot from 20 yards did not look like it would trouble Gordon but it bounced up sharply, forcing the keeper to punch the ball away.
At the other end David Meyler shot wide of the near post while Dowie's final roll of the dice was to bring on striker Mark Cullen for his first Premier League appearance on his 18th birthday.
The Hull fans gave a hearty cheer when Bruce was sent to the stands for one comment too many to the officials, but they knew their fate and the final whistle brought resignation as a number of home players slumped to the turf.