The wicket was flat and the tourists took full advantage after winning the toss and electing to bat.
Warner's 135 punished a wilting South Africa attack that lost Dale Steyn after lunch when the world's top Test bowler limped off complaining of pain in his right hamstring.
He will be assessed on Sunday to see if he can continue bowling in the innings.
Captain Michael Clarke (92 not out) and Steve Smith (50 not out) put on 114 for the fourth wicket and will resume on the second morning as they seek to bat the home team out of the match.
Warner, who raised the ire of South Africans after the second Test in Port Elizabeth by suggesting they had tampered with the ball, smashed 12 fours and a six in his 152-ball stay at the crease.
He recorded his seventh ton before falling to a catch behind by wicketkeeper AB de Villiers off spinner JP Duminy.
Paceman Steyn had picked up the first wicket, having opener Chris Rogers (25) caught at second slip by skipper Graeme Smith.
Alex Doolan then made a patient 20 off 66 deliveries before losing his cool as he tried to pull Vernon Philander, spooning a catch to Steyn at mid-on.
Only Morne Morkel with his steep bounce troubled the Australian batsmen, especially Clarke.
Morkel hit him on the elbow, gloves and the back of the helmet during a spell of ferocious fast bowling.
The series is level at 1-1.
Image: David Warner
Photograph: Carl Fourie/Gallo Images/Getty Images
South Africa fired up to end 44 years of agony against Australia
Smith expects even contest on Newlands wicket
Did South Africa indulge in ball-tampering in 2nd Test vs Australia?
No panic in Australia camp before final Test, says Harris
South Africa beat Pakistan to lift the Under-19 World Cup