Nielsen (86*) came to the crease late in the day’s first session with the West End Redbacks teetering at 4/34 chasing a target total of 170.
He and SA debutant Bosisto (47*) went on to steady SA’s innings, pushing the visitors to a deserved six-wicket victory just before tea on the fourth day of play at Blundstone Arena.
The win was the Redbacks’ first outright Shield victory since February of 2018 and vaults SA into fourth position in the 2019-20 Shield standings, now within nine points of second-placed Queensland.
The match finished with much-respected Tasmanian batsman George Bailey, who will retire from domestic cricket after this summer's Big Bash League to become a national selector, rolling his arm over.
Redbacks paceman Wes Agar, who ended Bailey's final Shield innings on Monday, was named Player of the Match after snaring career-best match figures of 8/121 including his maiden Shield five-wicket innings haul.
Agar and swing bowler Chadd Sayers made quick work of the Tigers’ tail in the morning to have the hosts all out for 261, setting up SA’s successful chase.
The Redbacks will reconvene after the KFC Big Bash break to take on Western Australia from February 14 next year in the State’s next Shield contest.