Joe Wenham (79) and Dave O'Brien (56) guided the visitors to a total of 217-8 from 44 overs, with the game having been shortened after an earlier rain interruption.
Lansdown's revised target was 225 and half-centuries from Joe Jenkins (58) and Jordan Price (55no) were not quite enough as they finished on an identical total to their hosts but lost by the Duckworth/Lewis system.
Lansdown finish the season with a tough trip to second-placed Taunton Deane on Saturday.