South African Abbott got the wickets flowing when he pinned Adam Lyth lbw, before New Zealander Hampton found Fin Bean slashing to point with his fifth delivery since becoming a late replacement for the injured Jack Edwards.
James Wharton was undone by some nip off the pitch from Brad Wheal to edge to third slip, before Bairstow arrived at the crease.
After 20 largely uneventful balls, exciting fast bowler Baker’s introduction – his first in the Championship brought drama.
Bairstow swatted a wide first delivery of the over to the fence, before his concentration was disturbed by an insect.
Baker’s follow-up was equally wide but this time Bairstow sliced to deep third man.
Dawid Malan had been the most lucid Yorkshire batter – striking six boundaries in his 31 – but ran himself out by taking on Mark Stoneman’s arm from extra cover.
The visitors made it to 106-5 at lunch, but after that they disintegrated. Abbott was relentless, while Dawson continued from his impressive 54-wicket 2024 campaign.
Ben Cliff was the last man out – lbw trying to reverse sweep Dawson – with the last five wickets disappearing in 27 post-lunch deliveries.
Hampshire’s response was solid as Stoneman and Fletcha Middleton produced a 70-run opening stand.
Former Middlesex left-hander Stoneman hit two legside sixes, summing up his approach to poor deliveries, but he was bowled by a George Hill inswinger before Nick Gubbins edged to first slip, White’s first Yorkshire scalp.
The White Rose then had their best spell of the day, with Ben Coad in particular, stemming Hampshire’s runs – typified by new batter Toby Albert taking 23 balls to get off the mark.
Middleton eventually fell to a bat-pad chance, with Bairstow leaping around the batter to make the catch in a short leg position.
Tom Prest made a brisk 32 before Hill set his off-stump tumbling and nightwatcher Brad Wheal was lbw as Hampshire reached the end of the day on 164-5.