The Tigers took regular wickets throughout the morning session to have the Monkey Towners 6-53, before eventually bowling them out for 143 at Cresswell Park on Saturday.
Jack Cattrall was once again the pick of the bowlers with 4-43, with Jim Allenby taking the new ball with success, securing three wickets.
The hosts are 2-115 in response, with some attacking stroke play from Travis Birt leading the top side. Claremont will be in search of an outright win next weekend.
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Subiaco Floreat will need a strong batting performance next weekend after a tough day in the field against Gosnells at Sutherlands Park.
Chris Hansberry was the pick of the bowlers with four wickets, including his 300th A Grade scalp, as Gosnells reached 287.
Cameron Green showed his potential with the ball following on from his hundred last weekend.
South Perth has set University a tough task after hitting 290 on day one of their clash at James Oval, with Josh Dallimore taking career-best figures for the home side.
Dallimore claimed 6-98 in a rearguard performance, with Rob Jones hammering a century. Harry Podmore bowled 28 overs for the day in a workman-like performance.