SCOTTISH international Don Hutchison repaid a huge slice of his £2.5m transfer fee with his first goals for Sunderland to set up a mouth-watering fourth round Worthington Cup tie against Manchester United.
Peter Reid's men had to thank Danish goalkeeper Thomas Sorensen for keeping them in the game at the Memorial Ground before Hutchison struck in the 48th minute with a stunning 25-yard drive.
Rovers looked as though they were going to take the game into extra-time when their dangerous teenage striker Nathan Ellington equalised.
Hutchison broke the hearts of the home fans in the 11,433 crowd with a match-winner two minutes from time.
Slovakian international Stanislav Varga, playing his first game for ten weeks after a serious leg injury, was quickly in action, stemming a couple of early Bristol advances.
Sunderland had Rovers in trouble in the second minute on a surface not helped by the torrential rain over the last few days.
Striker Danny Dichio was brought down 20 yards out, Michael Gray, playing on the left side of midfield, crashed his free-kick against the defensive wall.
Sunderland almost took the lead in the fifth minute when young striker Michael Reddy put a close-range shot against the foot of the post after Varga and Paul Butler headed on a left-wing corner from Gray.
Rovers, hestitant in attack, managed to force their way forward and Sorensen had to save on his line from Latvian midfielder Astafjevs.
Rovers had three men booked early on for fouls, Lewis Hogg, who crashed into Gray, and Che Wilson, who crudely brought down Chris Makin and then Mark Foran, for a bad challenge on Reddy.
Sunderland almost benefited from the third free-kick, with Hutchinson flicking Rae's left-wing centre inches wide.
Sunderland survived a scare when Sorensen again saved a long-ranger from Astafjevs and then hit back strongly for Nick Culkin to finger-tip a left-foot pile-driver from Reddy just over the bar in the 18th minute.
The game was surprisingly fast and skilful considering the treacherous surface and Sunderland looked the more assured side going forward with Reddy in particular was causing problems.
In the 25th minute he charged down a clearance and chipped the ball up for Dichio to have a close-range header pushed over the bar by Culkin.
Varga badly mistimed a challenge to send Nathan Ellington sprawling and there was danger from the freekick, with centre-back Steve Foster slamming a right-foot volley wide from the edge of the box.
Sunderland, however, looked the more dangerous side and were trying hard to create a clear-cut chance against a quick-tackling home defence in which Foster looked strong.
Ellington was Rovers' live-wire up front and after moving past Varga he was brought down by Gray for a free-kick which was curled wide of the angle from 20 yards by Wilson.
Sunderland almost went a goal behind in the 41st minute when a long free-kick reached Ellington and the striker's low right foot shot brought an excellent close-range save from Sorensen.
A lot of the sting had gone out of Sunderland's earlier play and Rovers were gaining in confidence.
Danish stopper Sorensen having to save at the second attempt from Astafjevs in first-half stoppage time, which ended with a booking for Hutchison, who fouled Simon Bryant. The home side opened the second half brightly, with Astafjevs testing Sorensen from long range - but Sunderland hit back to take the lead in the 48th minute.
Dichio laid the ball back to Hutchison, who cooly rifled in a tremendous right-foot shot from 25 yards, giving Culkin absolutely no chance with the power and accuracy of his finish.
The goal served to settle Sunderland and when they swept forward again a low centre from Oster was scrambled clear.
Rovers surged forward, however, throwing caution to the wind and Ellington almost came up with an equaliser as he swept a low shot into the side netting and then came a fierce barrage in which three shots were charged down.
The Rovers' pressure was rewarded with a controversial equaliser in the 63rd minute.
Sorensen went up for a high centre, but appeared to be fouled, losing his hold on the ball and Ellington slammed his shot into an unguarded net. Sorensen was left in a heap on the ground, but the referee waved aside protests to allow the goal to stand.
Sunderland brought on Darren Williams in place of Rae in the 72nd minute in a bid to stifle Rover's midfield thrusts, but Sorensen was still the busier keeper.
Rovers almost grabbed the lead in the 81st minute when central defender Jones rose high to a free-kick from the right and Sorensen responded with another great save, pushing the header over the bar.
Sunderland brought on leading scorer Kevin Phillips in the 83rd minute for Reddy and he almost made an instant impact when he nipped in to intercept a poor back-pass, but couldn't retrive the ball.
But Sunderland grabbed the winner in the 88th minute. Hutchison claimed his second goal with a close-range right foot volley after a centre from the left from young full-back George McCartney
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