Republic of Ireland international striker Long, who joined from West Bromwich Albion last month, made the breakthrough in the first half at the Stadium of Light after West Brown received a fourth-minute red card.
And former Everton striker Jelavic wrapped up three points in the 62nd minute to help Bruce seal a win against his former employers and leave the Tigers four points clear of the relegation zone.
“It’s great for them. The partnership is starting to flourish but they’re doing well individually, too,” Bruce told BBC Sport.
“They’ve done exactly what I thought they would do.
“There’s no egos, they’ve got great attitude, which is exactly what you need at a newly promoted club.”
We reorganised the team and, for some moments, we were still in the game but the second goal killed it
Meanwhile, Poyet was left to rue Brown’s red card for a tackle on Long and defensive errors as Sunderland’s good run came to an end.
“It’s something we’ve been good at in the last month and a half,” Poyet said.
“Before that, there was always something – a mistake or a sending off. We went back to that.
“It’s difficult to analyse. We tried. We reorganised the team and, for some moments, we were still in the game but the second goal killed it.”
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