Tambvekar ripped through the line-up with a stunning spell of 7-21, backed up by Jordan Price (1-23) and Reece Croker (1-15), as Shapwick were bowled out for 64.
Lansdown lost Jordan Smith for eight, but Joe Jenkins and Thomas Hankins remained unbeaten on 19 and 37 respectively to see them in with nine wickets and 40 overs to spare.