The West End Redbacks responded to Sunday’s loss to the Tigers at the same venue by racing to Tasmania's 255-run total in 38.4 overs for their second win of the Marsh One-Day Cup.
Australia's World Cup wicketkeeper Carey was in superb touch and hit the winning runs after a free-flowing and unbeaten 80 off 52 balls.
He smashed 13 fours and a six in a dazzling display, adding 130 runs in partnership with Head.
The captain also ended up unbeaten on 80 in a mature 99-ball knock.
Opener Jake Weatherald returned from a quad complaint in style with an important 53 off 57 balls, while Callum Ferguson contributed 28 alongside him at the top of the order.
Both teams entered the match with one win from three starts and in danger of losing touch with leading pair Western Australia and Queensland.
Tasmania opener Caleb Jewell hit a maiden century sharing a 162-run stand for the third wicket along with Jordan Silk (87).
Cameron Valente (2/40) and Kane Richardson (2/59) did the bulk of the damage with the ball with leg-spinner Adam Zampa and young seamer Luke Robins prising one wicket apiece.
The Tigers lost 5/45 inside the final eight overs of their innings to give SA a strong run at victory.
The match completes the opening leg of the one-day competition for both teams.
The Redbacks will now turn their attention to their Marsh Sheffield Shield opener against reigning champions Victoria at CitiPower Centre in St Kilda beginning on Thursday, 10 October.