The Hampshire opener led the Sixers to a nine-wicket victory over the Perth Scorchers on Saturday, chasing a target of 168 with three overs to spare.
The Sixers might have finished the game more quickly, but with one run required for victory, batsman Daniel Hughes opted to settled for dot balls off the final three deliveries of the 17th over, in order to give Vince a chance at reaching his century at the start of the 18th.
However, the 29-year-old was denied that opportunity when Scorchers bowler Andrew Tye’s first delivery was called a wide, handing the Sixers victory.
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The Sydney outfit finished top of the Big Bash’s pool stage and booked their place in the final at the first time of asking.
Perth, whose players include England internationals Jason Roy and Liam Livingstone, will have another opportunity to reach the showpiece, when they face the winner of the playoff match between Brisbane Heat and Sydney Thunder on Thursday.