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."

The RAC said the higher prices were due to a combination of rising crude oil prices, and the devaluation of the pound after June's Brexit vote.
Average petrol prices rose by 4.4p to 116.7p per litre and average diesel prices rose 5.2p to 118.7p per litre.
The motoring body said these were the biggest monthly increases for three and a half years.
Its fuel spokesman, Simon Williams, said retailers had "no choice" but to put up prices on garage forecourts.
"The effects of the weak pound have really been felt on the wholesale market, and this, combined with an oil price at nearly double its lowest level in 2016, has put significant upward pressure on wholesale fuel prices," he said.
"Certainly, we are a long way from the remarkably low fuel prices enjoyed by families and businesses early in 2016, when the average price of unleaded was around 102p per litre and diesel was 101p," he added.
According to the RAC, the increases mean it now costs Â£64.20 to fill the 55-litre petrol tank of a typical family car.
Meanwhile it costs Â£65.25 to fill up a similarly sized tank in a diesel car.
The RAC suggested that the price of fuel might stabilise in the coming months.
"Opec, which represents some of the world's biggest oil producers, recently agreed in principle a cut in production," said Mr Williams.
"But a final deal is still to be agreed at an Opec meeting at the end of this month and, with some analysts suggesting a deal might yet stall, this leaves open the prospect oil prices might stabilise or even fall before the end of the year," he added.
Hampshire collapsed from 84-0 but then declared on 211-9 as Somerset took control on day one at Southampton.
[NEXT_CONCEPT]
Petrol and diesel prices rose sharply in October, said the RAC, taking them to their highest level since July 2015.