The hosts enter the festive period in the best position in a decade.
Welbeck struck on the 32nd minute after what had been a tempestuous opening third and Owen Coyle will have felt that his side could have just as easily taken the lead.
For Steve Bruce, the result sees his side enter the congested festive period with his team looking comfortable in a Europa League spot and largely has his defense to thank, with a makeshift back-line delivering a Herculaen effort to keep out Bolton's sustained aerial assault on their box.
The game opened with typical tenacity, with tackles flying in from the ever competitive Sunderland captain Lee Cattermole, as both teams struggled to sustain a period of possession in the opening exchanges.
Owen Coyle's side may have been lauded for their transformation from long-ball specialists to a style with a little more subtlety but it was a 50-yard ball, a more sparingly used weapon in the Trotters armory, nodded on by Johann Elmander that provided Martin Petrov with the games first chance, only for the Bulgarian to limply hit the ball into Craig Gordon's grateful arms.
Bolton continued to press and their advanced play inevitably left gaps at the back, upon which Sunderland's advanced trio of Bent, Welbeck and Gyan pounced. Danny Welbeck looked to have squandered a great effort from 10 yards out but was rightly ruled out for offside.
The to and fro nature of the opening quarter of an hour was nearly summed up by a Sunderland break, again by Richardson. The wingers pace down the left earned his side a corner from which the ball fell to Darren Bent who was unable to keep his curled effort down. In better form, you'd have expected the England international to have found the back of the net.
The hosts were forced to alter their game plan on the 20th minute, with influential Ghanaian John Mensah going off with a suspected hamstring injury, replaced by Egyptian full- back Ahmed El Mohamady, with Nedum Onuoha switched to center-half.
The clash remained on a knife-edge as the half hour mark approached, with Bolton playing the better football but equally susceptible on the counter attack. In-form Swede Johann Elmander should have done better with a free header from 10 yards-out but put his chance wastefully over the bar, with an effort that was typical of the tie's opening third.
Elmander's miss appeared to shocked the home side into life and with an air of inevitability, the Black Cats took the lead. Jordan Henderson providing a deep ball from the right to Darren Bent who saw his fine effort matched by a superb save from Jussi Jaaskelainen, who with some misfortune, palmed the ball to a stooping Danny Welbeck to nod home from six-yards out
Bolton so nearly equalized on the stroke of half time but were denied through no fault of their own. With the Sunderland defense unable to clear Martin Petrov's low, whipped corner, Zat Knight pounced, poking the ball goalwards only for Craig Gordon to pull off an almost impossible save, reacting instantly to knock the ball over the bar, in what was a moment of absolute quality.
The second half began controversially with Lee Cattermole, who had already been ruled out of Sunderland's next match against Manchester United with a booking in the first half, mistiming a challenge against Johann Elmander and was incredibly fortunate to escape his third red card of the season.
Despite the competitive edge being ever-present, the opening exchanges of the second-half lacked the quality of the first, with the ball rarely escaping the the center circle for a prolonged period as Owen Coyle's side struggled to break down a defensively solid Sunderland outfit.
The home side could have settled it on the 70th minute, as some wonderful build up play between Gyan and Henderson led to Darren Bent to fumble on the penalty box and Danny Welbeck,to slide an effort on to Jussi Jaaskelainen's left-hand post.
Sunderland continued to press, with pace down the flanks met by neat, intricate interchange in front of the Trotters box, with England international Henderson looking the most likely to find the killer ball to put the game to bed.
As the second goal failed to materialize, the Wearsiders looked increasingly fraught and Bolton ramped up the pressure to find the equalizer, with Cahill going close with five minutes to spare.
The visitors' desperation to level the tie was matched only by a fantastic defensive effort from Steve Bruce's side, who manfully fought against the ever-increasing tide of Bolton pressure, with Nedum Onuoha and Phil Bardsley particularly impressing at the heart of the back-line.
Substitute Ivan Klasnic squandered a number of fine chances late on, failing to connect with the balls that came his way and Sunderland held on to ensure that they would leapfrog the visitors into an impressive sixth place of the Premier League.
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