The Falcons looked to have it won but the Tigers, with a finals spot on the line, wanted it more as they surged back from 25 points down 10 minutes into the final term to win 9.15 (69) to 10.7 (67).
The Claremont victory ended the Falcons' nine-game winning run at home and denied Swan Districts a place in the finals.
While the match had no effect on the Falcons' second-place standing, it was not without its costs as Andrew Strijk (leg), Chris Keunen (leg) and Marcus Adams (concussion) were injured.
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READ NOWTrent Manzone (33 disposals) and Aaron Black (36 disposals) led the possession count for a third consecutive week.
Co-captain Luke Tedesco had 17 possessions in his first league game back from a calf injury.
West Perth are expected to face a Peel side depleted by rested Dockers in the qualifying final at Arena Joondalup on Sunday.
Fremantle coach Ross Lyon has flagged resting a number of top line players for the weekend's game against Port Adelaide, meaning many of the Thunder's Dockers affiliates could be promoted for AFL duty.
A Falcons win would have them face Subiaco at Leederville Oval for a spot in the grand final the following Sunday.