The 29-year-old, on loan with the Black Cats from Bournemouth, scored twice against his old club either side of an Aiden McGeady strike, before netting an own goal late on which had no bearing on the outcome.
Norwich were dominating proceedings early on, but Sunderland opened the scoring against the run of play 27 minutes in when Grabban ran behind the Canaries defence, latching on to a James Vaughan flick-on from a ball over the top, and poked home.
Midway through the second half Sunderland had their third, courtesy of Grabban heading home after good work from McGeady, who curled a pinpoint cross towards his teammate.
However, Norwich were given a minute chance of potentially mounting a comeback when, 79 minutes in, James Maddison's free kick was headed back across Sunderland's box and, as the visitors failed to clear it, Grabban inadvertently put the ball into his own net.
Nonetheless, the visitors were not largely troubled after conceding, and were able to see out the game to claim all three points.