With both sides desperate for a win to stay in the hunt for the Shield final, the Tigers batted diligently throughout the majority of the first day of play at Bellerive Oval.
But exciting seamer Nick Winter stepped up for the West End Redbacks in the dying overs of the third session to claim three wickets in quick succession and peg the home side back from 3-219 to 6-281 by stumps.
The 24-year-old finished with figures of 3-56 from 24 overs.
Fellow seamer Kane Richardson claimed 2-59 for the Redbacks while Daniel Worrall (1-59) broke through for the opening wicket of the day.
Half-centuries to Jake Doran and George Bailey were the highlights for the home side.
Doran (74) and captain Bailey (55) batted patiently to be the major contributors for Tasmania, sharing a 111-run stand for the fourth wicket.
No.3 Beau Webster set the standard early with a conscientious 42 but his dismissal left the Tigers wavering at 3-108.
Wicketkeeper Matthew Wade continued the momentum created by Doran and Bailey with a free-flowing 34 not out late in the day.
Tasmania received a boost before play with the inclusion of Jackson Bird, even though the fast bowler was ruled out of Australia's tour of South Africa through injury.