Starting the day 2-16, the Redbacks piled on 458 runs to be 8-474 at stumps with a 203-run lead on the back of effective attacking batting and erratic bowling.
Cooper made a brilliant 138, while Ferguson – who put on 73 for the third wicket with nightwatchman Joe Mennie (32) – added 101.
Ferguson then combined with captain Travis Head (66 from 61 balls) for a 122-run stand, with the skipper in an especially brutal mood. Head’s half-century came from 39 balls.
Aside from a sitter dropped by wicketkeeper Sam Whiteman when 80, Ferguson’s knock was faultless from someone pushing for Test selection this summer.
A steady 29 from Jake Lehmann then led into a commanding 198-run partnership between Cooper and Alex Carey.
Cooper and Carey had no trouble under lights, belting the WA bowlers around the WACA, with Cooper eventually falling with 23 boundaries to his name.
Carey was later out for a career-best 79.
Kane Richardson was six not out and Chadd Sayers eight at stumps.
Jason Behrendorff was the only effective WA bowler, with the left-arm quick taking 3-70, while Mitch Marsh had his moments claiming 2-84.
Another left-armer Ryan Duffield was especially poor conceding 88 in 13 overs with 16 fours off his bowling.