Long struck for the second time in as many games, after Wes Brown's fourth-minute dismissal, and Jelavic added a second 17 minutes after the break - his first Barclays Premier League goal of the season - with the depleted Black Cats unable to stem the tide.
Indeed, had it not been for keeper Vito Mannone and the woodwork, they might have won even more comfortably.
It was just the Tigers' second league victory in 12 attempts and it could hardly have been more timely after a return of just one point from their previous five outings.
But for Sunderland, a third defeat in 15 games in all competitions plunged them back into the mire from which they hoped they had escaped and with Manchester City, Arsenal and Liverpool to come away from home in their next three fixtures, things could get worse before they get better.
England manager Roy Hodgson was among a crowd of 42,810 at the Stadium of Light, but Adam Johnson's hopes of impressing him were undone by Brown's premature departure and the re-organisation it prompted.
Sunderland went into the game still revelling in their 3-0 derby victory at Newcastle, which handed them back-to-back league wins for the first time since April last year.
But they did so with both manager Gus Poyet and chairman Ellis Short warning that there was still much hard work ahead, and their caution proved to be prophetic.
Hodgson may have turned up to watch Johnson, but it was another England international who caught his eye, if for all the wrong reasons.
Just four minutes had elapsed when full-back Phil Bardsley played a dreadful back-pass which was intercepted by Long.
The Republic of Ireland international surged towards the penalty area, only to be upended by the sliding Brown, who was immediately shown a red card by referee Mike Jones.
It was the former Manchester United defender's third dismissal of the season, although one was rescinded on appeal, and Sunderland's sixth, three of them against the Tigers.
Poyet replaced wide midfielder Fabio Borini with central defender Santiago Vergini in a bid to reconstitute his defence, but it took a stunning 16th-minute save by Vito Mannone to deny Jake Livermore.
However, Sunderland failed to make the most of the Italian's efforts as they cleared the resulting corner only as far as the Hull midfielder, whose scuffed effort was glanced into the net by Long.
The home side, who were so impressive at St James' Park, were struggling to re-group and Mannone kept them afloat with another fine reaction save to claw Nikica Jelavic's 26th-minute corner out of the top corner.
But even he needed the help of his right post five minutes later when Long turned and drilled a stinging effort against the upright from 25 yards.
Chances at the other end were understandably fleeting with Vergini stabbing wide from Marcos Alonso's acrobatic volley within seconds of his arrival and Johnson thumping a 44th-minute volley straight into keeper Steve Harper's midriff.
But with Black Cats old boy Ahmed Elmohamady and Liam Rosenior terrorising left-back Alonso and Long making life intensely difficult for John O'Shea and Vergini, the visitors held the whip hand going into the break.
Defender Rosenior was replaced by midfielder Robert Koren at the start of the second half and Hull pushed forward in a bid to kill the game off.
Former Sunderland midfielder David Meyler passed up a half-chance when he failed to control Long's cross after good work by the excellent Livermore, and Koren blazed high and wide after a corner was cleared to him a minute later.
However, Sunderland remained patient and started to pass the ball, and after a concerted period of possession, Harper had to pull off a good save to keep out Ki Sung-yueng's deflected shot following Liam Bridcutt's intelligent pass.
Jelavic was unable to make the most of Meyler's 57th-minute through-ball as he shot harmlessly across the face of goal, but the respite was only temporary.
Poyet may wonder why full-back Maynor Figueroa was allowed to run from halfway and crash a shot against Vergini, and why Jelavic was unmarked as he leapt to head firmly past the helpless Mannone.
It was plain sailing from then on with the Black Cats seemingly resigned to their fate and the visitors in complete control.