Hampshire 223 and 111 for 3 (Weatherley 56) need 358 more runs to beat Nottinghamshire 302 and 389 for 9 dec (Mullaney 130, Taylor 83)
Vince, who played throughout the Ashes series despite only twice passing 25, returned to the Test side for the final Test in New Zealand and responded with a typically elegant 76.
But, despite some promising innings, Vince averages just 24.90 after 13 Tests. And, while concerns over his fragility around off stump remain, he cannot be assured of retaining his place when the squad for the Test series against Pakistan is named in a couple of weeks' time.
It was that weakness that Broad exploited here. An entertaining final half-four saw Broad, charging in from the Pavilion End, using all his skill and experience against a team-mate he had seen batting at close quarters for several months over the winter.
Having been beaten by one that bounced and left him early in Broad's spell, Vince was naturally reluctant to play at anything outside off stump. But with Broad persuading one to tail back in just a fraction, Vince's decision to pad up left the umpire with a simple leg before decision to make. For selectors undecided over Vince's future, it may prove a telling blow.
To be fair to Vince, Broad will trouble many batsmen in this form. He generated decent pace despite a surface that is now funereal and, having tinkered with his action ahead of the New Zealand tour, is gaining just a little more movement and bounce than has been the case for a year or so.
"He's really charged in," Nottinghamshire's captain Steven Mullaney told ESPNcricinfo after stumps. "He's shown his class and been magnificent.
"You have to pinch yourself sometimes to realise you're not watching it on TV; you have to actually catch it if it comes your way.
"He changed his action a little to get the ball moving away from the right-hander more and I think it's helped him get a bit more bounce, too. He's looking magnificent to the right-handers and that makes his inswinger all the more dangerous. He's bowling with really good pace and control."
That Nottinghamshire had an opening was largely due to the persistence of Harry Gurney and the inexperience of 21-year-oldJoe Weatherley who had batted with admirable composure in demanding circumstances. Despite a match situation that demanded he try and bat for the best part of four sessions - Hampshire had been set an improbable 469 to win in a minimum of 140 overs - the former England Under-19 captain had just recorded his maiden Championship half-century and, in batting for 34 overs, given his side an outside chance of saving the game.
But a momentary lapse of concentration cost him. Lured into a drive by Samit Patel's teasing spin, Weatherley lofted a simple catch to mid-on. For all Patel's skill - and this was a slightly quicker ball delivered with a rounder arm - it was an unnecessary stroke. It may console Weatherley a little that a batsman as experienced as Hashim Amla made a similar mistake on the previous day. But the manner in which he walked off - head in his hands, aghast at his error - suggested it may take some time for any consolation to sink in. He shaped up very nicely before that, though, and is probably one to keep an eye upon.
Gurney helped Nottinghamshire build on those foundations. Delivering an outstanding 13-over spell from the Pavilion End, he showed again the vast improvements he has made to his bowling over the last few years. Where once he was a raw and pretty unsophisticated left-arm quick bowler, he now operates off a short run, moves the ball both ways and retains the ability to deliver a sharp effort ball when required. Despite the emergence of Luke Wood and the return of Mark Footitt (who is currently on loan at Derbyshire and not guaranteed to come back), he remains the best left-arm seamer on the staff and retains a place in Nottinghamshire's best XI.
He was rewarded for his persistence with the wicket of Jimmy Adams. Having seen the batsman dropped at slip from the previous delivery, Gurney bowled another one in the same channel outside off stump and was delighted to see Mullaney, the culprit the previous ball, hold on.
Earlier Mullaney had become Nottinghamshire's first centurion of the campaign as he helped set an imposing total. With help from the wonderfully aggressive and selfless Ross Taylor (who made 83 from 69 balls), Mullaney took full advantage of easing batting conditions to stretch the lead well beyond 400. Liam Dawson, who only a year ago was being talked about as England's No. 1 spinner, bore the brunt of the assault in conceding 123 from his 24 overs. Patel, who has barely conceded a run an over throughout this match, could be forgiven for wondering what more he has to do to warrant a recall.
Vince had finished the Nottinghamshire innings as their stand-in wicket-keeper after Lewis McManus was obliged to leave the field having sustained a hand injury. Hampshire are awaiting the results of a scan, but confirmed that he will bat on the final day if required. Vince's late departure rendered that requirement almost inevitable.