Shane Long celebrates after opening the scoring [GETTY]
Jelavic ended his 11-month drought by netting in the second half to give the Tigers all three points.
The game was barely a minute old when Wes Brown was given his marching orders after bringing down Long on the edge of the area.
Sunderland were forced into a quick reshuffle and Fabio Borini was sacrificed with Santiago Vergini taking his place.
And Long put Hull ahead in the 16th minute when he followed up Jake Livermore's shot from range by deftly heading the ball past Vito Mannone.
Nikica Jelavic shows his relief after scoring his first goal in 11 months [GETTY]
Sunderland could have found themselves 2-0 down on the half hour mark when Long pinged a crisp left-footed drive from 25 yards that struck the bar.
Hull upped the tempo and they sealed the win when Jelavic guided home a header from 12 yards.
The result sees Sunderland lie just one point above the relegation spots.
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