The visitors trailed by as much as 44 points in the third term before gaining control and chopping the margin to 23 heading into the last quarter.
Coach Bill Monaghan sensed the match was his side�s for the taking, giving a purposeful three-quarter-time address. But the break proved favourable for the Tigers, with West Perth�s momentum broken when play resumed and Claremont holding firm to win 12.11 (83) to 8.15 (63).
The Tigers� performance suggested they have the potential to be a much better side than the bottom-placed ranking they held heading into the match.
It was a frustrating loss for the Falcons, who would have jumped from fifth to third had they won.
Instead they fell to seventh, with Swan Districts (fifth) and East Perth (sixth) ahead of them on percentage.
Co-captain Jay van Berlo produced his finest performance of the season with 21 disposals and a game-high three goals.
Seasoned footballer Ray Bartholomew kicked two goals, including a raking 50m bomb in the last quarter, to stake his claim for a place in the side, having been relegated to the Reserves since round two.
With the Falcons on equal points with the Royals, it places increased importance on victory in this weekend�s derby at Arena Joondalup, which will leave the loser a game outside the top five.