Needing to dismiss the Tigers for less than 299 to have a chance of reaching the Shield final, the Redbacks struck quickly on Sunday morning with Joe Mennie and Chadd Sayers doing the damage.
Callum Ferguson is optimistic his side's bowlers can get through Tasmania's batsmen in a day.
"With our bowling attack, we've got a lot of confidence in them, they've been fantastic over the past couple of years so we think that will be enough," he said.
Outsiders South Australia could still scrape through to the Sheffield Shield final but must first dismiss Tasmania for less than 299 runs in Hobart.
Batsman Callum Ferguson made 90 for the Redbacks in their second dig of 406 on Saturday, helping boost the visitors' chance of victory at Blundstone Arena with one day of play remaining.
At the same time in Brisbane, ladder leaders Victoria scored an innings and 11-run win over Queensland - a result that helps SA's bid for a finals berth.
"It's nice to see that result go that way but certainly we're firmly focused on this game at the moment," Ferguson told reporters.
"We haven't paid too much attention. There hasn't been too much chatter about those other games since early on day one.
"We did (consider all the scenarios) early in the week and then we thought, 'Actually, it doesn't matter what happens around the country. We've got to win our game first'."
The Redbacks also need Western Australia to beat or draw with NSW to keep their season alive.
But most important, SA's bowlers must dismiss Tasmania's entire batting order on Sunday.
"With the skill that we've got in our camp, we're confident that we can get the job done," Ferguson said.
After a lacklustre first-innings total of 225, to which Tassie replied with 332, SA's batsmen stood strong in their second dig.
A 173-run partnership by Ferguson and Tom Cooper underpinned the innings, with each notching up half-centuries along with opener John Dalton and No.9 Adam Zampa.
For Tassie on Saturday, Shield debutant Gabe Bell and Sam Rainbird shared the spoils, with four and three wickets, respectively.