The Black Cats chalked up a third successive win and condemned the Hatters to an eighth defeat in nine matches despite taking an early lead.
A goal feast looked imminent after both sides found the net in the opening ten minutes with only bad finishing keeping the teams deadlocked at the interval.
Stan Varga cut out an angled drive from Dean Morgan in the fifth minute but the ball rebounded to the Luton striker who left debutant Marton Fulop with no chance of making an instant impact.
Sunderland responded immediately with a fierce drive from Graham Kavanagh that whistled just past the post. But the Black Cats were not to be denied and in the ninth minute were on level terms.
Ross Wallace released Daryl Murphy who held off Leon Barnett and, although there was a suspicion of handball, the Irish striker blasted an angled left-foot drive into the roof of the net for his fifth goal of the season.
Barnett headed over when well-placed after the home failed to clear a free-kick and, when Markus Heikkinen was caught in possession, Murphy fired into the side-netting.
Morgan sent a vicious 20-yard dipping free-kick just over the top but Luton missed a great chance to regain the lead when Varga allowed a long ball out of defence to drop over his head and leave Morgan in the clear.
But with only Fulop to beat, the Hatters' leading goalscorer failed to hit the target.
Murphy had a thumping drive beaten out by Dean Kiely but, in an even contest, Rowan Vine was just too high and Fulop saved well from David Bell's free-kick.
David Connolly was even closer to a goal when he latched on to a back pass by Heikkinen only to be denied by the alert Kiely on the stroke of half-time.
It was Connolly, however, who put the Black Cats ahead in the 53rd minute with another stunning effort. Receiving from Elliott, Connolly turned smartly to drill the ball wide of Kiely into the bottom corner of the net.
Only a brilliant save by Kiely from Liam Miller prevented the midfielder giving Sunderland a two-goal cushion in the 57th minute. Connolly cleverly cut in along the by-line and, from his centre, Miller's effort was turned behind in style.
Fulop dropped an easy cross to cause panic in the home defence and was then relieved to see a Vine header flash across the face of goal when well-beaten.
Luton made a double substitution in the 76th minute, sending on Warren Feeney and Adam Boyd but, apart from Feeney lashing a cross over the bar late on, the home side held on for another hard-fought win.