After a replay, the winner will meet Sunderland in the quarterfinals.
Sagbo did well to control Sone Aluko's right cross and fire past Brighton goalkeeper Peter Brezovan. Aluko was making his first start in four months after recovering from an Achilles injury.
Leonardo Ulloa gave Brighton the lead on the half hour after a one-two with Will Buckley.
Ulloa should have doubled Brighton's tally on the stroke of halftime but headed wide of an open goal.
Sagbo and Curtis Davies hit the crossbar for Hull.