The hosts, who began the day on 2-53, were chasing 164 for a first innings triumph at Kingsway.
The match was still in the balance with the Roos at 8-140, but Fawcett (94) guided the side to victory with tailender Mathew Dzodzos (15).
Dzodzos fell with the innings secured at 9-183, Fawcett going on to an 85-run tenth-wicket stand with Chris Quelch (39) to have Wanneroo finish on 268 in the 82nd over.
Western Warrior fast bowler Andrew Tye took 5-39 as the Gulls’ best with the ball.
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Scarborough returned to the crease for the last 20 overs of the day, Anthony Del Borello making a quick 49 before falling to Matthew Leach (1-11).
The 10th-placed Roos face second-placed Melville on Saturday.