Joe Sayers hit 11 fours in his unbeaten 178-ball 74
Jacques Rudolph and Joe Sayers featured in their fourth century opening stand of the season as Yorkshire made smooth progress on day two at Headingley.
Sayers hit 74 not out in a 162-run opening stand with Rudolph (68) out of 169-1 in reply to Hampshire's 351.
It was a day when both sides were able to celebrate Division One survival.
Hampshire reached safety after securing a third batting bonus point, while the Tykes stayed up once Sussex had been bowled out for 243 by Nottinghamshire.
Former Yorkshire batsman Michael Lumb, was on 72 when Hampshire resumed in the morning on 227-4.
But it was Nic Pothas who monopolised the early scoring, taking two cover-driven boundaries off Matthew Hoggard in one over soon after the new ball had been taken.
Ajmal Shahzad - named at lunchtime as the Yorkshire players' player of the year - bowled splendidly from the Football Stand End.
And he broke the partnership at 260 when Lumb attempted to drive a full-length ball and was well held by Anthony McGrath at second slip for 81.
Hoggard then picked up his only wicket of the innings at a cost of 115 runs when Dimitri Mascarenhas chased a ball outside off-stump to provide McGrath with another excellent catch.
Hampshire reached safety at 301-6 before losing Pothas, caught behind off Deon Kruis.
Although Dominic Cork carefully accumulated an unbeaten 42, the tail quickly subsided with the last three wickets toppling in 12 balls for the addition of six runs.
Two of them fell to Shahzad, who finished with 4-75 to give the colt 40 Championship wickets this season.
Rudolph stroked cover boundaries off the first and third balls of the innings to get Yorkshire off to a confident start. But the runs suddenly dried up and it took Sayers 25 balls before he was able to sprint a single to get off the mark.
By then, he had already given a very sharp chance to Liam Dawson which the Hampshire man could not hold on to at third slip.
But Sayers quickly caught up with his partner after tea- and both batsmen reached their half-centuries in the same over from David Griffiths, Rudolph off 99 balls, Sayers from 123 deliveries.
Only two overs of the day remained when Rudolph departed for 68, deceived by left-arm spinner Danny Briggs into floating a catch to Tomlinson at mid-on.
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