The Hatters made a hefty six changes from the reverse at Bramall Lane, with Reece Burke suspended, while Sonny Bradley and Jordan Clark missed out due to injury.
Peter Kioso, Henri Lansbury and Allan Campbell dropped to the bench as in came Tom Lockyer and Glen Rea for their first starts since November 27, James Bree, Luke Berry, Gabe Oso and top scorer Adebayo returning too.
Town were almost undone from the first corner, James Shea beaten, but skipper for the night Kal Naismith was covering behind to head over his own bar, as City had the better of the opening stages, a much-altered Luton having an increasingly disjointed feel to them.
Another set-piece delivery midway through the first half saw the ball fall to Han-Noah Massengo who drilled over.
With the home crowd getting increasingly frustrated as passes went astray and Town lacked any real intensity out there, they finally had something to get excited about on 36 minutes, Adebayo nutmegging his man and winning a corner, headed disappointingly wide by Rea.
The high class delivery from Bree was to prove a theme throughout the match, as on 42 minutes, he was behind the opening goal, receiving a short corner back from Kal Naismith.
The full back swung in a deep cross which allowed Lockyer to power home his header at the far post for a first Luton goal, the defender enjoying his moment in front of the away fans who had given him merciless abuse at Ashton Gate in the previous fixture for his lengthy Bristol Rovers affiliation.
After the break, Town made a far brighter start, two good breaks leading to two corners, Bree's improved delivery forcing the visitors into some hurried clearances.
City got themselves on the front foot once more though and had the leveller they deserved on the balance of play, Osho not dealing with a long ball forward, Lockyer slipping, allowing Andreas Weimann acres of space to go through and coolly slip his shot beyond Shea.
The Luton keeper thought he had kept Town in front with a stunning stop from Cameron Pring, arching his back to flick his angled drive over, although an infringement in the build-up unbeknown to anyone had been spotted.
Jones responded by bringing on Fred Onyedinma and Campnbell, the former's first involvement to shoot low at O'Leary, while Osho's header from another good Bree corner was wayward.
Bree, who has clearly worked extensively on his set-pieces in recent weeks, was then the architect of Luton's second goal on 68 minutes.
From a free kick this time, he sent over another excellent delivery which led to an almighty scramble in the area and Adebayo eventually wheeling away to celebrate a 12th goal of the season.
Just when Luton looked to have got control, the Robins were inches away from a second equaliser, that man Weimann again spinning to fire narrowly over the top, sub Nahki Wells also going close in the latter stages.
The Robins should have snatched a leveller in stoppage time, Weimann who looked suspiciously offside for the second time in a matter of minutes in the build-up, left all alone in the box from Cameron Pring's cross.
He somehow put his free header across goal, Wells unable to turn the follow-up in, finding the side-netting.
Joe Williams then shot tamely at Shea from outside the box, as Luton dug in to ensure they had done enough to move back up to 10th ahead of a visit from title-chasing Blackburn Rovers this weekend.
Hatters: James Shea, James Bree, Gabe Osho, Tom Lockyer (Peter Kioso 86), Kal Naismith ©, Amari'i Bell, Glen Rea, Pelly-Ruddock Mpanzu, Luke Berry (Allan Campbell 61), Admiral Muskwe (Fred Onyedinma 61), Elijah Adebayo.
Subs not used: Simon Sluga, Henri Lansbury, Carlos Mendes Gomes, Dan Potts.
Robins: Max O'Leary, Jay Dasilva (Tommy Conway 85), Chris Martin, Callum O'Dowda (Joe Williams 76), Andreas Weimann ©, Cameron Pring, Antoine Semenyo (Nahki Wells 76), Tomas Kalas, Zak Wyner, Alex Scott, Han-Noah Massengo.
Subs not used: Daniel Bentley, Danny Simpson, Sam Bell, Ayman Benarous.
Booked: Berry 25, Semenyo 62, Pring 67, Kioso 90.
Referee: Geoff Altringham.
Attendance: 9,202 (586 Robins).