It took Hull until the 16th-minute to make their numerical advantage tell when Long flicked Jake Livermore's scuffed shot into the roof of the net.
The game was over as a contest when Jelavic headed past keeper Vito Mannone after Maynor Figueroa's 62nd-minute shot had looped up invitingly off substitute Santiago Vergini.
Asked if the win was all the sweeter because of the nature of his exit from Sunderland in November 2011, Steve Bruce said:
"A lot has been said. I have just said walking up the stairs, the last time I came here, I needed to have a police escort to get home.
"That was two years ago. A lot of water has gone under the bridge since then. I'm not going to be the last or first Sunderland manager sacked.
"It's no sweeter than winning anywhere, believe me. But it was the manner of it which pleased me today."