Vince, who lost his place in the England Test line-up after a disappointing winter in Australia and New Zealand, effortlessly collected 147.
His innings was backed up by Tom Alsop, who notched his 10th career half century, and Fidel Edwards’s best bowling figures for the county.
Edwards had been the main architect with his analysis of six for 50 as Nottinghamshire were bowled out for 166 in the morning session, with a deficit of 111.
But the afternoon belonged to Vince, who scored his first 50 from 65 balls to go alongside his first innings 74.
The prime attribute of Vince’s innings was his supreme sprinting between the wicket, which saw his score increase quickly and put pressure on both the fielders and the bowlers.
He had been brought to the crease in just the second over when Jimmy Adams was beaten by a swinging delivery from Mark Footitt.
Vince soon saw Joe Weatherley lbw to Matt Milnes and Sam Northeast caught behind off Steven Mullaney.
Vince offered no clear chances in his almost flawless innings, although popped up two leading edges either side of reaching his landmark to gaps in the field.
Nottinghamshire skipper Mullaney appeared lost for plans to dismiss the right-handed batsman, with three extra covers deployed at one stage in an attempt to lure a mishit drive.
Vince appeared in no mood to lose his wicket and reached three figures for the third time this season in 139 balls.
For all Vince’s guile, Alsop played the anchor for the partnership as he scored slowly, yet effectively.
He eventually reached a half-century in 112 deliveries, brought up with an out of place swipe over long-on for six.
Vince and Alsop collected career records, moving past 9,000 and 1,000 first-class runs, as the fourth wicket reached a stand of 171 before Milnes knocked over his off stump.
But the damage had been done with Hampshire reaching close with a lead of 364, with Alsop unbeaten on 63.
Nottinghamshire had started the day staring at a heavy first innings deficit after Edwards’ day one evening spell of three for nine.
And the West Indian didn’t let up in the morning as he struck in just the second over of the day, with Samit Patel failing to add to his over night total as he was lbw.
Edwards almost added Riki Wessels to his list of victims, but Rilee Rossouw spilled a regulation chance at first slip with the batsman on three.
Wicket-keeper batsman Wessels only managed another eight runs before Kyle Abbott struck him on the pads with a hint of nip back into him.
Nottinghamshire had needed somebody to steady the ship, like Vince had done in Hampshire’s first innings, and their own captain Steven Mullaney somewhat fit the bill.
Mullaney countered with 38 off 53 balls but before he could get away Gareth Berg teased him outside his off stump to edge behind.
Luke Fletcher continued the aggression with a quick-fire 43, which saw him smash Abbott for a maximum over mid-wicket alongside seven more bludgeoned boundaries.
But Fletcher failed to control a strike across the line against the extra pace of Edwards and skied to Liam Dawson at long-on.
Edwards completed his six-wicket haul by dislodging Matt Carter’s leg stump with a yorker, before he completed the Nottinghamshire innings by catching Billy Root at long-on.