Having won the toss and chosen to bat against the pink ball, the hosts got through the opening session untroubled.
But Craig Overton (2-35) struck, removing Jimmy Adams (47) and Rilee Rossouw in quick succession, before Jack Leach (2-54) and Tim Groenewald (2-27) hastened the decline.
Hampshire then put Somerset in to face six overs, but they closed on 18-0.
Overton, who was unused by England in last week's three-game T20 series with South Africa despite being called up to the squad, bowled a crucial spell to turn the tide.
With Liam Dawson (53) and Adams going well in their patient opening stand, the fast bowler found the latter's outside edge before Rossouw top-edged through to Steven Davies to go for a fifth duck in his last eight County Championship innings.
Dawson fell lbw soon after to Lewis Gregory (3-51) and, despite James Vince's 47, Hampshire's batting fell apart as Leach's accurate left-arm spin gave nothing away.
With a batting point secured, Hampshire captain George Bailey declared, but Marcus Trescothick (10 not out) and debutant Eddie Byrom, who was unbeaten on one, had no troubles reaching stumps under the floodlights.
Hampshire all-rounder Liam Dawson told BBC Solent:
"The crowds haven't changed. We haven't had any more people in. But it is early days and it is something that might work.
"From my first experience of it, they need to have a good look at what balls they are going to use. If you are going to keep on using those balls then you are going to get some pretty boring cricket.
"It was fine to see. It just goes very soft, very quickly."
Somerset fast bowler Craig Overton told BBC Radio Bristol:
"The ball was strange. It swings and then goes really soft. It didn't really do much maybe a little bit in it for the bowlers but because it is so soft and slow it is tough to score on.
"We knew it was going to be tough batting after lights so it is perfect to be nought down with Tres and Eddie.
"It was nice to be with the England boys and see how it all works. I've had a couple of experiences with it now and hopefully next time I'll get a go."
Hampshire collapsed from 84-0 but then declared on 211-9 as Somerset took control on day one at Southampton.