The visitors were 5-98 at stumps on Wednesday at Bellerive Oval, needing another 173 to win, after Matt Short and nightwatchman Todd Murphy were dismissed in the last three overs of the day.
Victoria needed Short and opener Marcus Harris to bat through to stumps, but Short chased Bell's delivery outside off stump and did not move his front foot to the drive.
He was filthy with himself after wicketkeeper Jake Doran took the simple catch to remove him for 17 and leave Victoria 4-98.
Murphy did not survive to stumps, edging a delivery from Riley Meredith to captain Jordan Silk at first slip for a duck.
Harris was on 39 and Liam Blackford yet to score - barely surviving a couple of superb deliveries from Meredith in the last over of the day - while Bell had taken 3-22.
Bell had a top day - he contributed an unbeaten 35 at No.10, his highest first-class score.
Victoria paceman Harry Hoekstra also continued his fine Shield debut as Tasmania were dismissed in their second innings for 236. No.7 Nikhil Chaudhary top-scored with 81.
The left-arm opening bowler took 4-52 to back up from his five-wicket haul in the first innings.
Hoekstra made his Shield debut last week, top-scoring in Victoria's first dig with 45 and then taking 6-103 as SA won by an innings.
Tasmania resumed at 4-39 and Hoekstra made the first breakthrough. Ben McDermott launched into a full-blooded drive, but Short took an excellent catch at cover to remove him for 33.
That left the home side teetering at 5-75 and it was a big wicket, given McDermott's first-innings ton.
McDermott and Jake Doran had been the only Tasmanians to reach double figures to that point in the game. When Murphy trapped Doran lbw for 47, Tasmania were 5-125.
But Chaudhary made sure they would set the Vics a target of 270 - the highest innings total of the game - hitting six fours in his 123-ball knock as Bell kept the tail wagging.
Bell then shone with the ball, dismissing Campbell Kellaway for a duck.
When he also had Victorian young-gun Ollie Peake caught behind for a six-ball duck, the visitors were in all sorts of strife at 2-6.
Test veterans Harris and Peter Handscomb knuckled down and put on 66 for the second wicket.
Just when they looked well-set, Handscomb hit a pull shot off Meredith down Chaudhary's throat at deep square leg. While his 39 off 59 balls was valuable, Handscomb blew his chance for a big score.
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