The skipper’s knock of 103 helped the Ageas Bowl side to an overnight score of 302 for six against the Red Rose.
Rilee Rossouw also impressed with the bat and will remain unbeaten this morning on 54.
Former England international Graham Onions (four for 64) was the pick of the Lancashire bowlers, removing Joe Weatherley (nought), Jimmy Adams (44), Tom Alsop (24) and Ian Holland (15).
Both sides are struggling near the bottom of the division one table and a win for either will be crucial in the fight to avoid relegation.
Vince feels the game is in the balance but reckons Hampshire can put themselves in a decent position if they notch a first-innings total of 400 tomorrow.
The Ageas Bowl captain said: ‘The game is probably in the balance I would have thought.
‘A decent pitch and I think with the new ball there was bit of extra bounce, some variable bounce and decent carry for a used wicket.
‘It seemed pretty flat until lunch and afterwards they got the ball reversing and there was enough to keep them interested.
‘It’s a good pitch. I found it quite tough early with the new ball.
‘The ball was bouncing a fair bit and kissing off the wicket and as the ball got older it became easier paced.
‘There was movement in the air after lunch in that initial 45-minute period and then Jimmy got out.
‘We’re still in a position where we can get 380 or as close to 400 with the bat as we can.’
Onions also believes neither side have an advantage yet.
He said: We are trying our best to get results and today has been a lot of character in what we’ve shown.
If we could have got one more (wicket) we might have said it had been our day.’