The former Cambridge United forward decided an eventful South Coast derby by heading the winner four minutes into injury time.
It took Revell's tally to four goals in two games after he also scored in Saturday's defeat at Yeovil.
He is back in the Brighton side after Bas Savage rejected a new 18-month contract and seized his opportunity to keep Bournemouth in the drop zone.
Revell opened the scoring in the 15th minute from close range from a cross by strike partner Nicky Forster.
Bournemouth levelled in the 24th minute when the Brighton defence failed to deal with a corner and Jean-Francois Christophe headed in a centre from Jo Kuffour.
Max-Alain Gradel clipped the bar with a free-kick from long-range for the visitors, before Revell rifled Brighton back into the lead in the 58th minute.
Bournemouth seemed set to gain their first away point in five matches when they pulled level again with 11 minutes left.
Kuffour's shot was saved by Michels Kuipers, but Sam Vokes played the ball back in for substitute Brett Pitman to pounce from close in.
Brighton's poor recent League run of just one victory in seven matches looked like continuing until Revell popped up again to thump in a header from a Jake Robinson corner.
It was welcome relief for manager Dean Wilkins who, as well as losing Savage, has also seen Matt Richards and George O'Callahan go back to Ipswich after loan spells.
Wilkins said: "It feels as though it has almost been us and the players against the world at the moment, so to come through the game victorious at the end gives us great pleasure.
"We are not going to hide behind the performance, which at times was patchy, but having been through what we have been through the determination, effort and passion the players have shown for the club has been immense."
Angry Bournemouth boss Kevin Bond raged: "We brought about our own downfall three times.
"The winning goal was diabolical. We had the ball from a throw-in, needlessly gave it away and for the umpteenth time could not defend a set-piece. It was nothing short of disgraceful."