Hampshire were bowled out for 341 by Glamorgan as they bid for their first LV County Championship win in seven matches.
Unbeaten overnight, Liam Dawson (72) and Adam Wheater (43) were two of the second day's first three wickets to fall after Hampshire resumed on 254-5.
Danny Briggs's unbeaten 26 helped ensure a third batting point at Cardiff's Swalec Stadium.
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