The hosts got off to a nightmare start as they were reduced to 10 men after just four minutes, with Wes Brown dismissed for hacking down Long on the edge of the area when the Hull striker was racing through on goal.
Things went from bad to worse for Gus Poyet's side as Long then put Hull into a 16th minute lead, heading home from close range after Jake Livermore had guided the ball back towards goal.
Hull had a number of chances to double their lead with Vito Mannone denying Livermore with a smart save before a stunning strike from Long cannoned back off the post from range.
Jelavic doubled the visitors' lead just after the hour mark with his first Hull goal when Maynor Figueroa's strike deflected into his path and he reacted well to head past Mannone and into the top corner.
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.
After a dreadful back-pass from Phil Bardsley, Long intercepted and surged towards the penalty area, only to be upended by the sliding Brown, who was immediately shown a red card by referee Mike Jones.
Poyet replaced Fabio Borini with central defender Santiago Vergini in a bid to reconstitute his defence, but it took a stunning 16th-minute save by Mannone to deny Livermore.
However, Sunderland failed to make the most of the Italian's efforts as they cleared the resulting corner only as far as the 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 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.
Sunderland remained patient and started to pass the ball and Harper had to pull off a good save to keep out Ki'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 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.