The Durham attack couldn’t remove Jimmy Adams or Liam Dawson in the first session with spells on a wicket that wasn’t doing much.
Scott Borthwick made the first breakthrough, striking with the second delivery after the lunch break with Dawson at short leg by Joe Coyne on 70, leaving Hampshire 171-1.
A boundary from Adams saw him pass the century mark, off 236 balls including 19 boundaries. He was out shortly after on 105, becoming Borthwick’s second wicket, when he was caught by Plunkett with the final delivery of the 77th over.
Myburgh (42) was out next ball, trying to drive a Blackwell delivery but sending it into the hands of Michael Di Venuto in the slips instead.
Hampshire passed the 250 mark with a boundary from former Durham overseas, Neil McKenzie, and at tea the hosts were 275-3.
James Vince (14) was the next man out when he was impressively caught by Stokes in the covers trying to drive a Blackwell delivery.
Some aggressive bowling from Liam Plunkett finally rewarded him with a wicket when McKenzie is caught behind on 43 as Hampshire stood at 312-5.
With no result likely both captains shook hands with six overs to go, agreeing on the draw. Hampshire finished with 345-5.
A post match interview with Geoff Cook is available to watch at www.durhamccc.co.uk/durhamtv/interviews
Highlights of all days play at The Rose Bowl are online at www.durhamccc.co.uk/durhamtv/highlights