Set 337 runs to win, Tasmania finished 8-308 in a tense draw at Adelaide Oval.

Doolan made 116 on Thursday's final day to follow his unbeaten 170 in the first innings.

The elegant right-hander put the visitors on track for victory: they were cruising at 3-240 with 23 overs remaining.

But Doolan's dismissal swung momentum, triggering a collapse of 5-53 to give the Redbacks a whiff of victory in the last hour.

Tasmanian stalwart George Bailey (32 not out) and tailender Lawrence Neil-Smith (one not out) navigated the last seven overs to deny SA.

The Redbacks' victory prospects appeared remote until Doolan, Ben McDermott (42), Test captain Tim Paine (one), Jackson Bird (six) and Alex Pyecroft (13) fell in rapid succession.

Doolan, who faced 604 balls across both innings, had earlier put on a 95-run stand with Beau Webster (40) as the Tasmania's sought a second win of the Shield season.

Test batsman Matthew Wade cracked 38 from 37 balls before being caught attempting a reverse sweep, before Doolan and McDermott featured in a 53-run partnership.

Doolan then feathered an edge to the wicketkeeper from the bowling of Wes Agar (3-49) and the tide turned, with McDermott out soon after.

Tasmania required 74 runs with five wickets in hand from the final 15 overs in the last hour, with stalwarts Bailey and Paine at the crease.

But the Test skipper was soon bowled by Nick Winter (2-41) and Bird was caught at deep square leg four overs later, leaving SA seeking three wickets in the final 12 overs to win.

Bailey found an ally in Pyecroft, whose cameo again lifted Tasmanian hopes.

But Pyecroft was dismissed with 41 balls remaining, forcing Bailey and No.10 Neil-Smith to shut up shop and extend SA's winless streak in Shield cricket to 17 games.

Australian Associated Press