The 24-year-old brought up his 11th first-class century, putting the Redbacks bowlers to the sword on a tame pitch.
He helped take WA to 5-381 at stumps. Will Bosisto is eight not out.
There was a tense moment for everyone at the WACA Ground when Bosisto was hit hard on the helmet by a Mennie delivery.
A concussion test found there was no issue and the all-rounder smacked a boundary the next ball.
Earlier, fellow Test hopefuls Shaun Marsh (17) and Cartwright (35) were dismissed too soon.
Captain Mitch Marsh rocketed to 95, which included 14 fours and 2 sixes, before attempting one too many pull shots and getting caught behind off Daniel Worrall.
It has been tough going for South Australia's bowlers. Mennie had two wickets but has conceded 114 runs in 20 overs.
WA suffered a blow before the game with left-arm quick Jason Behrendorff ruled out with lower grade back soreness. He joins fellow pacemen Nathan Coulter-Nile on the sidelines.