It took a 23rd minute Michael McGrath free-kick and some solid second half defending for the Bulls to beat a now fifth-placed Mangotsfield United side in front of a crowd of 602 at Cossham Street.
And similarly for Tivvy, Jamie Short`s 75th minute effort sealed their victory at Yate Town.
Mangotsfield lost fourth place to Swindon Supermarine, who beat Slimbridge 2-0 at the Webbswood Stadium. Connor Waldon put `Marine in front after 38 minutes and his second on the hour-mark proved decisive.
Tuesday`s other game saw bottom-markers Bridgwater Town lose 1-0 at North Leigh, for whom Roger James broke the deadlock seven minutes from time.
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