Pelly-Ruddock Mpanzu's first goal of the season, a trademark shot from outside the box, proved the difference between the sides as Town reinforced their position in the play-off places, remaining fourth with Middlesbrough beating Blackpool.
Manager Rob Edwards made one change to the side that beat Cardiff 1-0 in midweek to move into the top six, with Allan Campbell coming in to midfield and replacing Cauley Woodrow, who was amongst the substitutes.
Cody Drameh started for the second match in succession, whilst fellow January arrivals Marvelous Nakamba and Joe Taylor are on the bench.
James Shea is in the matchday squad for the first time since Cardiff in April year, with Jack Walton missing out after picking up an injury in training.
The Hatters made a dream start when Mpanzu picked up a lay-off from Elijah Adebayo in the middle of the Stoke half before driving forward and unleashing a 25-yarder with his right-foot that beat Matija Sarkic into the bottom corner.
It might have been two on 11 minutes when Alfie Doughty delivered a deep corner from the right that Tom Lockyer hit first time on the volley, but City midfielder Lewis Baker slid in to clear the danger in his own six-yard box with Sarkic at full stretch.
The visitors survived a shout for a penalty when Jordan Clark appeared to be pulled back by Josh Tymon as he made his way into the box by the right byline, but in the 22nd minute they sounded their first warning shot, Baker curling just wide of Horvath's post after Dujon Sterling had tricked his way past Doughty to cross from the right.
Town top scorer Carlton Morris fired inches over on 27 minutes after picking himself up from a heavy challenge 25 yards out, before Drameh had to stand tall to head a dangerous looking free-kick whipped in by Baker.
The Hatters continued to pose more of a threat, and with ten minutes to go the break Amari'i Bell let fly with a 35-yard pildriver that Sarkic did well to hold under his crossbar, although the visitors' keeper dropped a high free-kick from Clark under pressure from Adebayo, but the Town striker couldn't get his shot on the turn past the Montenegro international.
Drameh became the first player into referee Dean Whitestone's book for a late challenge on Tymon, who after a lengthy period of treatment was carried off on a stretcher to applause from all sides of Kenilworth Road, being replaced by Ki-Jana Hoever.
The opening period of the second half was end-to-end, without either side really creatng a clear-cut chance, although Adebayo's pressing in the box almost forced Sarkic into a mistake when charging down the goalkeeper, the ball missing the goal and flying behind for a goal kick.
Stoke had the ball in the net on the hour when a Tom Lockyer clearance flew high in the air, and although Ben Wilmot's header flew in, ref Whitestone had already blown for a foul by Josh Laurent on Horvath as the Town keeper looked to come to claim the ball.
Edwards made his first changes straight afterwards, with Nakamba and Onyedinma - so impressive down the right when he came on for his return from injury against Cardiff in midweek - on in place of Campbell and Drameh.
With 20 minutes to go, it was Woodrow's turn to enter the fray for Morris, who had worked tirelessly up front with Adebayo, but Stoke were starting to look dangerous, Bersant Celina clipping a ball over the top for substitute Tyrese Campbell to volley over.
Clark was soon picking the Stoke midfield's pocket and setting Adebayo running into the box, but former England international Phil Jagielka got back to smother the ball behind before the Town man could get his shot off.
Woodrow found space on the right to cross low for Clark to steer a shot on goal, but straight at Sarkic with just over ten minutes remaining. Then, in the 81st minute, the former Fulham and Barnsley man met Doughty's left-wing free-kick with a glancing header that travelled past the far post.
The victory made it back-to-back home wins for the first time this season, as Luton remain fourth in the Sky Bet Championship.
Attention now turns to the Emirates FA Cup, where Edwards' side have the opportunity to make it into the Fifth Round where a tie against Southampton awaits.
Goals:
Mpanzu (6)
Att: 10,031 (1,021 away)
