High-flying Lansdown ravished the Frome line-up to secure a dominant win.
After a middling start that saw them reach 48-3, wickets fell at regular intervals for Frome.
Mark Sanger (3no) and Clive Hamblin (17) showed some resistance, but the recovery they threatened never materialised as they were dismissed cheaply.
Lansdown looked to make short work of the run chase, playing aggressively from the start.
Frome's solitary wicket was that of Joe Jenkins for 12, caught by Sanger off Eddy Neal.
However, an unbeaten 53 from Jordan Smith and 23 not out from Tom Hankins saw Lansdown comfortably across the line.