Jack Smallman kicked a 68th-minute penalty to clinch promotion for Chichester and leave them on the brink of the London Four South East title.
Chi, who won Sussex One last season, came through 20-17 in a highly competitive tussle at Crawley.
They will clinch the crown if they beat Guy's Hospital at Oaklands Park a week on Saturday.
Long-serving prop Frank Corby admitted: "It was a very hard fought game but a great result for us."
Smallman scored a try and kicked a conversion. Mark Webster and Ben Polhill also got over while Simon Bradford had an exceptional game.
Lee McDonagh scored a Crawley try and also charged down a kick for Richard Billings to power over.
Andy Evans converted both and kicked a penalty in a stirring display by the home side.
Bognor are one win from claiming the second promotion place and skipper Karl Flynn admitted: "We will be happy with that."
Lee Williams crossed twice and wing Billy Toone claimed a first senior try in a routine 32-7 win at Guy's Hospital.
Paul Mitchell, Chris Pinchbeck and Stuart Pearce also crossed with Gareth Williams adding a conversion.
Hove lost 32-7 at home to Old Dunstonians. They were 17-0 down but Phil Ward's try, converted by Martin Lovell, hinted at a comeback.
Lock Nick Evans scored Heathfield's try but a spirited display could not save them from a 13-5 defeat at Beccehamians.
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