Barnes-Homer joined Luton from Kidderminster in November
Luton's Matthew Barnes-Homer scored a minute after coming off the bench to cut Stevenage's lead at the top of the Blue Square Premier to two points.
The substitute curled in a left-footed shot from the edge of the box to earn the Hatters their eight straight win.
Stevenage striker Tim Sills had earlier had a goal ruled out for offside, while George Pilkington had an effort cleared off the line for the visitors.
Sills, Charlie Griffin and Mark Roberts wasted late chances but Luton held on.
Second-placed Luton's victory on their first visit to Broadhall Way ends Stevenage's unbeaten home record.
But the Hertfordshire side still remain well placed for promotion to the Football League with a game in hand over their Bedfordshire neighbours.
Luton made the brighter start, Tom Craddock forcing home goalkeeper Chris Day to save and Michael Bostwick making a goal-line clearance from Pilkington.
After a goalless first half, Luton keeper Mark Tyler made a fine save to deny Chris Beardsley just minutes before Barnes-Homer entered the fray.
The former Kidderminster Harriers man was then introduced as a replacement for Craddock by Hatters boss Richard Money, who had already taken off his other striker Kevin Gallen at half-time. And Barnes-Homer made an immediate impact, firing past Day.
Graham Westley's Stevenage, who were unbeaten in 11 games, wasted chances in the latter stages. But they were unable to prevent Luton and their 2,800 visiting fans celebrating that eighth straight win.
Stevenage Borough boss Graham Westley said:
"It was an even contest. I said to Richard Money at the end that the best side lost and he agreed.
"The lads are gutted. It was our first defeat at home since November 2008 and there's always a small sense of injustice after losing when you think you're the better side.
"It could easily have been a different result. We've had a goal disallowed and then they've nicked it. But tense affairs like this are often settled by one moment like that.
"We have to pick ourselves up and kick on."
Luton Town manager Richard Money told BBC Three Counties Radio:
"Matthew Barnes-Homer's been in good form in recent weeks in training and was very good in the reserves in midweek.
"And I thought it was sensible to bring someone like Liam Hatch on. Kevin Gallen wasn't happy but Hatch gives you a different threat.
"It's nice to be able to call upon those two. Tom and Kevin have been on fire but today was not their day but Matthew and Liam are arguably as good and it worked for us.
"It takes all kinds of things to get a performance. Sometimes it's free-flowing football. Other times, you need to make sure we defend well, win the headers, make the blocks and get the tackles and it was that type of game."
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