Resuming on 43-1 after there was no play in the first session, debutant Eddie Byrom (43) and Adam Hose (48) put on 77 to take the score to 102-1.
But Holland then dismissed Byrom, James Hildreth, Tom Abell and Steven Davies in a remarkable four-over spell of 4-8.
He ran out Lewis Gregory before Gareth Berg (3-26) claimed two wickets, then rain forced an early close at 135-8.
Somerset came into the day in a commanding position, having triggered a similar collapse from Hampshire with the pink ball under the floodlights in their first innings.
However, the poor middle-order batting that has undermined their County Championship season came back to haunt them, meaning a first win of the season is now very unlikely.
Opener Byrom, who had looked otherwise solid, chipped USA-born Australian Holland to mid-on and Hildreth went lbw for two before Abell and Davies feathered edges to Lewis McManus, both without scoring.
Gregory was run out by Holland when he slipped trying to run a quick single, leaving Berg to pin Hose lbw and have Craig Overton caught at mid-wicket before rain prevented any play in the final session.
Ian Holland told BBC Radio Solent:
"It was a strange session of cricket. Obviously they had the momentum early and they got a decent partnership but we got a load of wickets in a hurry, so it's a decent end for us.
"It puts us in a strong position. You never know. There are still 96 overs, maybe more, left in the game.
"It is nice to contribute and come in and do well. I don't want to come in and be deadweight. The pink ball has been good to me. It seems to do bits in periods of the game and then flatten out. You are never out of the game."
Somerset director of cricket Matt Maynard told BBC Radio Bristol:
"It was so good to see Adam Hose and Eddie Byrom batting well and getting into a good position, then Holland came on and nipped it around under the lights and caused problems.
"It was nibbling a little bit more. When you come in under those conditions it is tricky. He had a couple of decent balls out there. None of our boys gave their wicket away.
"Eddie Byrom has impressed full stop. I liked the look of him in the academy and he is now getting his game. He knows his strengths in this form of the game and he showed that with the balls he left. I feel chuffed for the lad."

Jones, 33, announced his retirement after being left out of Wales' 2015 Six Nations squad.
Gatland says he would have "preferred" Jones to delay his decision until after the 2015 Rugby World Cup.
"I was as surprised as anyone when Adam made the decision to retire," said Gatland.
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"I would have preferred it to have been perhaps after the World Cup because he wasn't out of contention in our minds in terms of the World Cup."
Tight-head Jones made 95 appearances for Wales, winning three Grand Slams, and played five Tests for the British and Irish Lions over two tours in 2009 and 2013.
The former Neath and Ospreys player's last appearance for Wales was the 38-16 defeat by South Africa in the first Test of their June 2014 tour.
His Test future was cast in doubt after he was replaced by Samson Lee after just 30 minutes of that game, having struggled in the scrum.
He was then left out of Wales' autumn 2014 series and was placed on standby for the Six Nations in case of injury.
Gatland at the time said that the door was open for Jones to force his way back into the squad for the World Cup, but the prop said that he made up his mind before Christmas that if he was not chosen for the squad he would retire.
Jones is set to continue playing for Cardiff Blues, who he joined on a one-year deal in August 2014 after his Ospreys contract expired.
Wales, meanwhile, kick off their Six Nations campaign at home against England on Friday, 6 February.
"As a coach you've got to make some hard calls sometimes and we've been very pleased with the progress in particularly Samson Lee over the last 12 months," explained Gatland.
"But sometimes you make that call when you're looking for some depth in certain positions.
"He's [Jones] made that decision to retire and we have to respect him for that."
Ian Holland took 4-16 as Somerset collapsed, losing seven wickets for 33 runs against Hampshire on day three.
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Wales coach Warren Gatland says he was surprised by the timing of prop Adam Jones' retirement from international rugby.