They could have found themselves in even worse straits, having teetered on the edge of humiliation at 2 for 4 and then 29 for 7 before late blows struck by Shaun Udal and, especially, Nixon McLean helped the last three wickets to realise 75 runs.
Forced to follow-on, Hampshire made a better fist of things second time around but may struggle to take the match into a fourth day.
The largest damage to their first innings was inflicted by Chris Silverwood, who could have done little more to advertise his qualifications for an England call. The 23-year-old, who toured the West Indies but was not chosen for any Tests, finished with 5 for 13 from 10 overs.
He bowled with pace and accuracy as batting proved no less hazardous than it had on the first day, the ball swinging in the air and moving off the seam. Three of his victims were leg-before. Paul Hutchison, the 21-year-old left-armer, claimed 3 for 49, figures that would have looked somewhat more impressive had his last three completed overs not cost 41.
The bowler of the moment earlier had been the Hampshire all-rounder Dimitri Mascarenhas, whose exploited the conditions with his right-arm medium pace as Yorkshire, 242 for 3 overnight, lost six wickets for 30 runs. Mascarenhas ended Matthew Wood's fine innings at 108, then blunted Bradley Parker's progress before removing Richard Blakey and Richard Stemp with consecutive deliveries, finishing with 4 for 31.
But David Byas's strategy in declaring 20 minutes before lunch proved to be inspired. Aided by a good catch by Stemp in the gully, Silverwood dismissed Giles White with the sixth ball of his first over and trapped Robin Smith and Derek Kenway with the fourth and fifth balls of his second. It was an inauspicious maiden Championship innings for Kenway - and on his 20th birthday.
With John Stephenson driving Hutchison to backward point, Hampshire lurched to lunch at 3 for 4 and reeled on into the afternoon as Adrian Aymes and then Mascarenhas fell to Silverwood, the latter facing 38 deliveries without scoring.
When Kevan James departed to Gavin Hamilton's first ball, Hampshire were 29 for 7 but a flurry of boundaries from Udal, one of which freakishly found its way into a spectator's holdall, and McLean, who hit two sixes off Hutchison and a third off Hamilton, transformed their total into something comparatively respectable.
The early dismissal of Stephenson as Hampshire followed on, 223 behind, conjured thoughts of the debacle being repeated but although Smith played on to Hamilton, White survived a chance to Byas at second slip on 18 to compile a face-saving half-century before also playing on, to Hutchison.Reuse content