SA were travelling along well at 1-80 before James Pattinson and Jon Holland (1-28) made a triple breakthrough to leave the home side 4-82 at lunch.
It was a blow to the Redbacks who had consolidated after the early loss of opener McInerney (12), caught at second slip off Pattinson.
Head (67) then shouldered the bulk of the responsibility with a gritty half-century against an in-form Victorian attack.
He was supported by Andrews (59) who is playing just his second game back in the side this season after last week's nine-wicket match haul against the Queensland Bulls at the Gabba.
He showed his quality with the bat, with a second first-class 50 and a 51-run partnership with fellow bowler Winter (21) which helped his side to 260.
Seamer Winter snared SA's first wicket four balls before stumps, making the dangerous Marcus Harris edge behind for 16.
Victoria are 1/28 after the first day, 232 runs in arrears of South Australia's first innings total.