Rotherham were the dominant force in the first half but Luton pushed on after the break, with Collins turning in a Luke Berry free-kick for the only goal.
Berry also hit the post as the Hatters secured a fifth win of the campaign, leaving their opponents to rue missed chances as they stayed two points above the relegation zone.
Story of the match
Luton boss Nathan Jones made six changes to his starting line-up in response to defeat at Brentford last weekend, as well as returning to a back four, but his side were outplayed for most of the first half as Rotherham set the tempo, despite the early setback of left-back Joe Mattock’s innocuous injury.
Jamie Lindsay, inspired by an unlikely two-goal salvo in his previous home game against Sheffield Wednesday, was twice denied by impressive Simon Sluga saves. The first stopped an out-swinging shot from the edge of the box which was aimed right for the top corner, and the second saw the Croat nudge his effort from a Wes Harding cross round the post.
Michael Smith also had a couple of good opportunities but couldn’t stretch Sluga with either, shooting into the ground from a Florian Josefzoon cross and then heading a Dan Barlaser free-kick straight at the goalkeeper.
Luton were providing only had the most sporadic of threats on the counter, only registering their first shot in the 43rd minute when Jamal Blackman made a fantastic reaction save to deny George Moncur after Harry Cornick squared the ball. That sparked a late flurry from the Hatters, with Sonny Bradley heading wide from a corner and Matty Pearson shooting the wrong side of the post from distance.
Rotherham started the better side again in the second half, with Smith’s head failing to convert two more glorious chances before he was hooked off. But Luton soon grew back into it, and twice in a couple of minutes were wondering how on earth they hadn’t taken the lead.
First Moncur played the ball across goal and Collins appeared to have a tap-in, but having overrun the ball slightly he couldn’t get the right contact on it to prod into the net and it diverted behind off a defender. Moments later, Blackman missed a cross into the box after Cornick aimed towards the net, but Michael Ihiekwe was back on the line to save the day.
Berry had a powerful strike deflected wide and the tide was clearly turning in favour of the visitors. So it proved with 20 minutes remaining, when Berry delivered a free-kick from the right and Collins got ahead of his marker George Hirst to strike the ball past Blackman.
With the Millers forced to push, Luton exploited the space left behind. Moncur should have scored when played through on the counter by Pelly-Ruddock Mpanzu but tamely passed the ball straight into Blackman’s chest, before Berry turned Ben Wiles inside out and struck the post.
Rotherham had some chances to salvage a point late on, but Barlaser skied an effort and Hirst sent a bullet header wide.
Jones rings the changes
Jones didn’t mess about after last weekend’s surrender against Brentford, making six changes to the starting line-up as well as returning to the back four with which they finished that game having experimented with a five in previous games.
There were rare league starts for the likes of Ryan Tunnicliffe and Moncur, with the latter providing a dangerous threat – even if he really should have scored in the second half.
Collins also returned to the striker’s position which has been rotated over recent matches and was combative throughout, and a smart piece of play and finish earned his side the win. He’s their top scorer with five goals, though this was his first strike since the opening day of the league season.
The midfield would have been less pleasing for the manager, outrun and outfought in the first half. Joe Morrell was brought off at the break for Mpanzu, who was a real game-changer with his attacking thrust as Luton turned the tide.
But the biggest positive of the night will be the defence, which held together strongly despite its makeshift nature to secure a clean sheet. With it they earned a third win in Yorkshire already this season, and they will remain up north until Saturday’s game against Huddersfield Town confident of making it four.
Smith fails to step up
The hectic schedule forces managers into changes to freshen up the squad, and Smith was tasked by Paul Warne with leading the line for Rotherham in place of Freddie Ladapo.
Smith had a point to prove having struggled so far this season, but could hardly have had a worse night. He could not complain about a lack of service with no fewer than four excellent chances, but failed to seriously test goalkeeper Sluga with any of them.
He was withdrawn before the hour mark was even reached, by which time the damage was done as Luton hit the front and took advantage of those missed chances with their own centre-forward proving more clinical.
Not only has Smith failed to score yet in this campaign, but on each of three occasions he has started in the Championship this term the Millers have failed to hit the net at all, losing each time.
He was one of only two changes – Warne admitted after that he perhaps should have freshened things up further – with the other seeing Wiles return. He was back in central midfield but only lasted a few minutes before Mattock’s injury saw him moved to full-back, where he again showed his value in versatility.
Man of the match: Sonny Bradley (Luton)
Bradley excellently led a makeshift backline consisting of midfielder Glen Rea alongside him in the middle, centre-back Pearson on the right, and right-back Martin Cranie on the left, as Luton managed to secure a clean sheet.