Yorkshire’s mammoth 593-9 declared left them with two-and-a-half days to bowl out the visitors twice, and get their bid for a third successive title up and running.
But after one-and-a-half of them, the home attack was off the required pace as Vince (119) and Ervine (123) extended the rearguard to 450-8 in this Division One match.
Yorkshire mustered only the wicket of the Hampshire captain in the first two sessions, their toil under sunny skies and on a docile pitch culminating in the sight before tea of occasional spinners Adam Lyth and Gary Ballance bowling briefly in tandem.
By then, the heavyweight attack which racked up 45 bowling points out of 48 last summer had already dropped the first of the new season.
Vince had done much of his hardest work on the way to 76 the night before, and cashed in on a deserved 18th first-class hundred - in front of appreciative national selector James Whitaker.
There was more at stake, of course, than Vince’s Test aspirations when he and Ervine resumed on a highly-vulnerable 141-5 - with the follow-on target of 444 a distant notion.
Vince began by driving the first ball of the morning for four off Jack Brooks, an accurate portent for much of the remaining action.
It featured great determination from Ervine - who needed a five-minute time-out, pain-killers and then an x-ray at stumps after taking a blow on the left hand from Liam Plunkett when he had just 20 to his name.
Vince had hit 16 boundaries by the time he lined up no shot to a predicted outswinger and had to go lbw when instead Steve Patterson slanted one in.
Plunkett ensured most discomfort in an aggressive six-over morning spell from round the wicket, but the nearest he came was when Ervine propped one just in front of short-leg on 22 - with captain Andrew Gale marginally on his heels.
Yorkshire were therefore soon pinning plenty of hopes on the second new ball, either side of lunch. It was to no avail, with conditions vastly in the batsmen’s favour.
After their own chastening experience in the field at the hands of three Yorkshire centurions, Hampshire were in no mood to pass up the opportunity.
Adam Wheater contributed 62 runs and a further 47.2 overs of support for Ervine, in a partnership of 143, before he chipped Patterson tamely to midwicket.
Yet still Yorkshire’s progress stalled.
Ervine reached three figures from 205 balls, and appeared set to close out the day with minimal alarm until Ryan Sidebottom (three for 78) found the edge behind to keep the follow-on temporarily in the equation.
The Zimbabwean was the 1,000th wicket of Sidebottom’s career, across all formats, putting him in rare company on a day when Yorkshire had little else to celebrate - especially after an unbroken stand of 59 between Ryan McLaren (55no) and Chris Wood.
Yorkshire: Lyth, Lees, Ballance, Gale (captain), Bairstow, Leaning, Rashid, Plunkett, Patterson, Brooks, Sidebottom.
Hampshire: Carberry, Alsop, Vince (captain), Smith, Dawson, Ervine, Wheater, McLaren, Wood, Tomlinson, Edwards.