A stunning century from Travis Head was not quite enough to save South Australia's season as Tasmania held on for a 16-run victory which keeps their JLT Sheffield Shield final hopes on track.
Chasing 331 to win on the final day at Blundstone Arena, bottom-placed SA appeared on track for an unlikely win before eventually falling to defeat when they were all out for 314.
In terms of runs, it's Tasmania's third narrowest Shield victory ever and the equal 26th smallest margin of victory in the competition's history.
Tasmania face holders Victoria next week with a spot in the final on the line in a winner-takes-all final-round contest in Hobart.
"Four wins is probably a little bit above expectation to where we thought we would be at this stage, so we are really happy with that," Tasmania coach Adam Griffith said.
"The confidence is good and they are enjoying their cricket which is probably the biggest thing, and that was something that was probably (previously) lacking in the group."
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 and scored 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 in pursuit of 331 to win.
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 slip off Sam Rainbird with SA 19 runs short of victory. Winter was the last man out, with Test quick Jackson Bird claiming his fourth wicket to secure the win.
Bird took six wickets in his first match back from a hamstring injury and shapes as a key figure for the Tigers' Shield run-in.
"It's pretty handy having a Test cricketer to run in and take those wickets," Griffith said.
"He was really good towards the end and bowled well.
"He was a bit rusty with the hamstring injury, so he will take some confidence from that game."
While happy with his seventh first-class century, Head lamented both the narrow defeat and the team's inconsistent form this season.
"To get where we did today was great but I'm pretty disappointed personally that I couldn't give us the opportunity to win the game," he said.
"We have had some close games where we haven't quite been able to get over the line but we have been pretty inconsistent at times, so it has been a pretty up and down season."
Tasmania: Alex Doolan, Jordan Silk, Beau Webster, Jake Doran, George Bailey (c), Matthew Wade (wk), Simon Milenko, Tom Rogers, Sam Rainbird, Jackson Bird, Andrew Fekete
South Australia: Conor McInerney, Jake Weatherald, Callum Ferguson, Travis Head (c), Jake Lehmann, Tom Cooper, Alex Carey (wk), Joe Mennie, Kane Richardson, Daniel Worrall, Nick Winter