The Republic of Ireland winger, still to win over hordes of the Wearside Army, curled home an exquisite shot on 40 minutes to dent determined Derby.
Fans favourite Kevin Phillips rediscovered his scoring touch to net only his second goal of the season to double the lead, before Sunderland had to withstand a frantic last seven minutes after Malcolm Christie chipped home for his fourth goal this campaign.
The win was doubly rewarding for Sunderland boss Peter Reid, forced to field a side blighted by nine absentees.
Without a victory since day one of the season, Reid has stuck by £2.5 million signing Kilbane throughout his struggle to settle.
The home side made the early running, but cavalier Derby, with Horacio Carbonari and Georgi Kinkladze making their first starts this season, came back at their hosts.
Dean Burton fired over when well placed before Christie was denied by a brilliant right-hand reaction save by Thomas Sorensen, back in the starting line-up after injury.
The opening goal came at the other end though as Chris Makin picked up the ball halfway inside the Derby half then fed Kilbane, who sped past two defenders before unleashing an exquisite left-footed curling shot past the flailing Mart Poom.
The Black Cats, who twice hit the bar through Don Hutchinson, extended their lead through Phillips after a deft one-two with strike partner Niall Quinn, before Christie's left-foot chip made for a tense finish.
However, there was no way back for Jim Smith's Rams side, who remain desperate for their first three points of the season.
Sunderland: Sorensen, Makin, Gray, Craddock, Thome, Kilbane, Williams, Hutchison, Arca, Phillips, Quinn. Subs: Macho, Holloway, Roy, Oster, Thirlwell.
Derby: Poom, Bragstad, Elliott, Higginbotham, Eranio, Valakari, Johnson, Carbonari, Kinkladze, Christie, Burton. Subs: Schnoor, Sturridge, Morris, Murray, L. Grant.
Referee: P Taylor
