Head has posted a compelling century off 200 balls against a powerful NSW attack on the second day at Adelaide Oval.
The West End Redbacks are 7-222 at stumps after bowling the Blues out for 289, with paceman Chadd Sayers collecting a career-best 8-64.
Sayers' figures are the best by a South Australian since Jason Gillespie's 8/50 in 2001, and they are ninth-best in SA Shield history.
Tom Cooper's 37 also ensured the veteran batsman passed 5,000 Shield runs for the State since his first-class debut in 2008.
Head's composed 214-ball innings featured nine fours but he was dismissed just three overs before stumps by Josh Hazlewood, while Tom Cooper (37) was the only other batsman to pass 20.
The 25-year-old Head's 11th first-class century came against a Blues bowling line-up featuring Test stars Hazlewood (1-58 from 20 overs) and Nathan Lyon (1-42 from 20).
Head's knock is timely for both his Test prospects and his state, but the young captain said post-play that he is solely focussed on keeping the Redbacks in the game.
NSW debutant Daniel Solway top-scored with an unbeaten 133 and Peter Nevill made 53 in the first innings.