Cleeve slipped to seventh in B&D Division Two after losing by five wickets to Brislington seconds.
Put into bat on a damp pitch, they lost captain Glenn Lewin to a 12-ball duck.
Young Ben Jones dug in with James Cole, who hit six fours in his 31.
And Sam Williams helped Jones (14) move the score along before drinks.
Williams fell to a yorker for 14 after the restart, with Mitch Want (11), Nikhil Bhajipale (12), Tom Birt all following.
Joe Hance, Max Viney and Dan Dixon fell cheaply to leave Tom Carpenter stranded as Cleeve were all out for 114 in the 40th over.
Lewin and Hance failed to make a breakthrough in reply, but Cole (3-26) and Bhajipale (2-30) had some success as Brislington eased to victory inside 30 overs.
Cleeve are due to visit Bohemians on Saturday, while the seconds return to action after a blank weekend with a home match against Bohemians seconds.
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