Championship promotion hopefuls Brighton went ahead when Argentine Leonardo Ulloa started and finished an incisive move after half an hour but Ivory Coast striker Sagbo's smart control and shot five minutes from time levelled matters.
Poyet left Brighton last June after a clash with the board and in October joined top flight strugglers Sunderland, who are already through to next month's last eight.
Hull, without cup-tied strikers Shane Long and Nikica Jelavic, hit the woodwork twice and now face the burden of an extra game as they try to stay out of the relegation zone, which they are three points above with 12 games left.
(Writing by Mark Meadows; editing by Ken Ferris)
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