South Australia have pulled off one of the most remarkable wins in the Sheffield Shield's 132-year history, beating Tasmania by two runs on the final ball of the match.

Tasmania required four runs from the last delivery in Hobart on Monday to reach their mammoth target of 429 for a dramatic victory.

Riley Meredith hit to deep cover, but with the ball fielded he came back for a second and was run out after being sent back by batting partner Lawrence Neil-Smith.

The last-ball wicket allowed South Australia to claim the equal-tightest Shield victory ever in terms of runs, in a match that went past 6pm on the final day.

Making the win even more remarkable is the fact that Tasmania had looked in the box seat to claim the victory before losing 4-4 from the final nine balls of the contest.

The win put SA top of a cluttered Shield table, while Tasmania are now last.

"I thought we were gone, then back in it, then gone again and back in it," South Australia's captain Ben Manenti said.

"I was content with the draw more than anything.

"But Wes nailed six beautiful yorkers back to back. Forty minutes ago I thought they would (win) it five down.

"Realistically we needed two wickets and they needed six runs. They could have hit six singles to the deep guy and walked it home.

"Hell of a game of Shield cricket."

After Tim Ward's 142 had appeared to put the hosts in a position where they could not lose the match, Mitch Owen and Brad Hope gave Tasmania a real chance of victory in the final session.

Owen blasted 53 from 39 balls, while Hope finished on 69 in a 72-run partnership that lasted just 10 overs.

Hope was eventually caught on the boundary trying to hook Wes Agar, but with Owen firing the Tigers still looked a chance.

Tasmania required 62 from nine overs, 44 from six overs, and then seven from nine balls after Owen hit Nathan McAndrew deep over the mid-wicket rope.

But when Owen was caught on the long-on boundary a few balls later and Matt Kuhnmann was out first ball, South Australia were back in the game.

With seven still required from the final over and two wickets in hand, Gabe Bell was bowled by Agar for a duck before the last-ball madness ensued.

The earlier stages of the day had also been full of drama, with Ward's century his first since his maiden Shield ton in October 2021.

With Jake Weatherald and Jordan Silk each hitting 65 for the Tigers, Ward struck 16 boundaries in his knock, including a cracking cover drive off Agar to bring up his ton.

But the left-hander was caught up in one of the more bizarre moments of the game in the middle session.

With Tasmania flying in the chase, South Australia resorted to short-ball tactics to try to slow the momentum.

Ward ducked a bouncer off Henry Thornton, scratched out his guard and walked out of his crease in scenes reminiscent of the Johnny Bairstow-style stumping at Lord's last year.

Much like Alex Carey last July, SA's wicketkeeper Harry Neilsen threw down the stumps.

On this occasion the appeal was denied, with umpires having seemingly decided over had been called.