Pakistan-born Ahmed, who recently made his Australian T20 and one-day debuts in England, went for 20 in a loose first over at Bankstown Oval on Tuesday.
However, Ahmed (4-38 off 8.2 overs) smashed through the middle and lower order and recorded career-best one-day figures.
Tasmania were well placed at 2-143 in the 34th over, with Ed Cowan (60 off 88 balls) prominent, but the Tigers lost 8-54 to be dismissed for 197 in the 49th over.
In reply, Victoria achieved their target with 5.1 overs to spare after a slight mid-innings wobble.
Wade and David Hussey (9 off 14) were both run out, as the Bushrangers lost 3-19 and slumped to 4-101,
Handscomb and John Hastings (23 not out off 26) completed the task.
Ahmed concentrated on bowling at the stumps after a first over he admitted he took too easily, as Cowan belted him for a six and two fours,.
"The guys really supported me and boosted my morale, especially the captain and that was the turning point for me," Ahmed said.
Pakistani refugee Ahmed continued his super run in 2013 after an initially frustrating period as he waited to be granted Australian citizenship following his arrival in the country in 2010.
"Cricket is a funny game, sometimes it favours you, sometimes it makes you cry, but its a good time for me," Ahmed said.
"It took a long time to come to this stage. I've been through a really tough time, but to be honest the last year has been amazing."
Tasmania suffered another dramatic collapse after losing 8-46 in Sunday's tournament-opening 81-run loss to NSW.
"I need to be held accountable for that and probably needed to bat a little bit longer through the innings," Cowan said.
Cowan added 76 in just under 14 overs with captain George Bailey (29 off 41).
At one stage the wind was so strong the umpires removed the bails from both sets of stumps, before replacing them with heavier ones.