The Roos, who amassed 190, had Melville at 9-91 when play was abandoned in the 25th over of the one-day match at Kingsway.
This left the visitors with a revised target of 182 to win, of which they had fallen 91 runs short.
The Roos were dismissed in the 48th over of their innings, with WA-contracted opener John Rogers providing a strong knock of 73 and number four Jake Fawcett adding 31.
Melville bowler Mark Turner took 6-28 to be his side’s main threat with the ball.
It was a shared effort within the Wanneroo bowling attack as Gary Atkinson (2-20), Chris Quelch (2-27) and Donavinn Fryer (2-36) worked hard for two wickets each.
The win advanced Wanneroo to third place heading into the club’s away clash against Subiaco Floreat on Saturday.