Vince may be out of the England reckoning at present, but his 171 in Hampshire's semi-final total of 348 for nine at Southampton was a reminder of his talent.
It proved all too much for visitors Yorkshire, who had five players away on England duty for the one-day international series with Australia.
The White Rose could only manage 241 in reply, with Hampshire and England spinner Liam Dawson taking four for 47.
"It is very pleasing," said Vince, whose side will play Kent in the June 30 final. "We set a big score and then came out with the ball and set the tone early. It means a lot to get to Lord's. At the start of the tournament I got a couple of fifties but never got a big one, so to get a big one in the last one and this one is nice.”
Vince, batting at number three, went to a hundred off just 83 balls before his second six, struck over long-on, took him to 150 in style.
He was eventually caught in the deep off Adam Lyth.
Yorkshire suffered a setback in their chase when India batsman Cheteshwar Pujara was undone by a rising delivery from South Africa fast bowler Dale Steyn that took the shoulder of the bat before finding its way to Jimmy Adams at second slip.
Vince had the last word in the match when, at mid-off, he caught Ben Coad off Chris Wood.
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