The three-time winners led the Rebels until the 59th minute but could not score in the final 20 minutes, bowing out of finals contention with one regular round left.
The Rebels scored three tries to two in their first win in seven matches against South African opposition and it was their seventh win of a much improved season.
There was some controversy with the Bulls denied a try by centre Burger Odendaal in the 61st minute after adjudication by the technical match official in the stands.
Odeadaal appeared to ground the ball over the try-line but the TMO thought otherwise after video replays and disallowed the try.
The early exit from the Super Rugby season will increase pressure on coach Frans Ludeke after a second straight season where the Pretoria-based Bulls have missed out on the finals.
The Bulls are still without a win in Australasia for over three years.
The Bulls began strongly with prop Dean Greyling scoring in the fifth minute only for the Rebels to hit back with a well-worked try off a scrum win for No.8 Sean McMahon.
The South Africans kicked away to a 17-7 lead in the 30th minute with a try to blindside flanker Pieter Labuschagne off the back of a rolling maul.
But fly-half Jack Debreczeni scored right on half-time for the Rebels to get within three points of the Bulls.
Fly-half Jacques-Louis Potgieter kicked the Bulls to a 20-14 lead with a penalty goal just after the resumption, but that was to prove the South Africans' last points of the match as the Rebels began to dominate possession and territory.
Giant lock Lopeti Timani crashed over in the 59th minute and Mike Harris converted the try to edge the Rebels into a 21-20 lead heading into the final quarter.
The Rebels had the ball deep in Bulls' territory when the clock wound down to see out a tenacious win.
“We've worked hard and we've given it our all, but obviously not enough so we have to work in this last week to get some results out of this competition,” Bulls skipper Pierre Spies said.
“I must give credit to the Rebels, they kept pressure on us and we couldn't get out of our half for a very long time and they also put pressure on our scrum.”
The Bulls will finish their season next week against the Central Cheetahs at home, while the Rebels finish at the home against Western Force.– AFP
Original source: Rebels end Bulls’ play-off hopes