Settling for a draw was especially frustrating in the end, given that a rush of wickets with the second new ball offered a fleeting chance of victory.
Having edged in front to lead by 27 with four wickets in hand at the start of the final hour, Hampshire lost Paul Whitaker to a Paul Hutchison yorker, Shaun Udal leg before to Chris Silverwood and then Nixon Mclean, who stretched the lead with two handsome cover drives before skying a return catch in the same over.
When Peter Hartley joined Kevan James at nine down, Yorkshire would have had every chance of winning were they to have shot either out quickly, with seven overs' batting time left to chase a mere 40-odd runs. But, much as Silverwood and Hutchison strained, the last wicket proved beyond them.
Yorkshire were effectively denied by an innings of resolute resistance mounted by the Hampshire wicketkeeper, Adrian Aymes, who had arrived at the crease with Hampshire 93 for 3 on Friday evening.
Resuming with the total 109 for 3 and the deficit 114, Aymes stood firm until 10 overs into the last session, stretching his occupation to almost four hours. He anchored partnerships of 59 for the fifth wicket, with Dimitri Mascarenhas, and 63 for the sixth, with Paul Whitaker. He ultimately fell to Richard Stemp.
Without Darren Gough and Craig White for their next Championship match against Durham at Chester-le-Street, starting tomorrow, Yorkshire are likely to be frustrated too in their request to England to release Silverwood from the 12 for the second Test.