Chasing 331 to win on the final day at Blundstone Arena, South Australia appeared on track for a famous victory before being eventually dismissed for 314 just 16 runs short of the Tigers' total.
Resuming at 1-49, SA's task seemed impossible after losing key men Jake Weatherald (17), Callum Ferguson (11) and Jake Lehmann (seven) inside the opening half-hour to be 4-69.
However, Head launched a counter attack scoring at a run-a-ball for much of his innings, before bringing up his ton off 123 deliveries.
Tom Cooper contributed 38 and Joe Mennie made 28, but their dismissals left SA's hopes resting on their captain as the Redbacks slipped to 8-255.
Head resumed his attack on the bowling and, with the help of rookie fast bowler Nick Winter (25), SA edged closer with a 57-run ninth-wicket stand.
Head, however, eventually fell for 145 after edging a catch to slips off Sam Rainbird, with SA 19 runs short of victory.
South Australia's tail was unable to finish the chase.
The Redbacks host Western Australia at Gliderol Stadium in Glenelg from next Wednesday in SA's final match of the 2017-18 Sheffield Shield season.