The skipper blasted 171 runs as Hampshire posted 348 for nine.
They then bowled out Yorkshire for 241 to win easily and reach the final of the Royal London One-Day Cup on Saturday, June 30.
Vince said: ‘It is very pleasing. From the word go we were very good.
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‘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. We haven’t been good in the 50-over competition in recent years.
‘It is always a special day out and I’m sure it will be a tough game against Kent.
‘At the start of the tournament I got myself in but never got a big one, so to get a big one in the last one and this one is nice.
‘It was a very good pitch to bat on which helps and once you get into a partnership you can get positive. I was able to free myself up at the end.
‘Me and Sam (Northeast) built a nice partnership together and hit the accelerator at the right time.
‘It really helps when someone at the other end can hit the ball over the ropes as well.’
Skipper Vince was elegant and dazzling for his 171 as he took his side towards a first Lord’s final since winning the tournament in 2012.
Liam Dawson picked up four wickets to complete the 107-run victory.