The Tigers were sent in by the Redbacks, posting 6-315 before dismissing the Redbacks for just 186.
Nick Winter struck early in Tasmania's innings to dismiss McDermott LBW for 0, before Ben Dunk (45) and Alex Doolan (62) recovered well.
But it was George Bailey (86) and Matthew Wade (46) who contributed a telling 125-run partnership at the back end of their innings. James Faulkner also provided a late cameo of 34 not out off 19 deliveries.
Spinner Michael Cormack picked up two wickets, while Joe Mennie was economical with 1-37 off his 10 overs.
In reply, Callum Ferguson top-scored with 43 for the Redbacks and Alex Carey scored 41.
But Ben Dunk (3-14) and Cameron Boyce (3-27) helped the Tigers bowl out their opponents inside 40 overs.
The Redbacks next face the Victorian Bushrangers at North Sydney Oval from 10:30am (local).