An 88th minute goal from Juma Omar helped Edu Rubio’s side to victory in a match in which their opponents from Gloucestershire dominated.
The Dons, who had never played Cheltenham at Under-18s level before, saw their visitors have the best opportunity of a first half in which limited chances were created.
A corner from the left saw a header hit the bar before the Dons survived a goalmouth scramble to maintain parity in a half in which they had been outplayed.
The hosts were restricted to mainly long-range efforts, which either went wide or proved comfortable saves for the Robins keeper, with left-back Joe Evans having the pick of the shots.
A golden chance was let slip by the Dons in the 53rd minute as a square ball from captain Hugo Logan from the right was crucially intercepted by the Cheltenham keeper with yellow shirts lurking in the vicinity.
Then, 10 minutes later, the home side had another good chance as a corner was played deep and headed back across goal by Brandon Thomas-Asante. In what seemed slow motion, the ball hit the base of the right post before bouncing away to safety.
The Robins continued to pose a real threat and on 72 minutes they had the ball in the net but the effort was disallowed – a corner from the right was headed into the net from around the penalty spot but the goal was chalked off because of a push in the back.
The visitors were continuing to press for a winner and they hit the woodwork again when a dipping free-kick ricocheted off the right hand post.
The game was becoming increasingly stretched and on 87 minutes an effort from outside the area from Logan caught the top of the crossbar on its way over with the goalkeeper beaten.
With two minutes remaining, the Dons broke the deadlock as a corner was flicked in at the near post by centre-half Omar, sparking wild celebrations from the home players who went into a jubilant pile near the goal.
In stoppage time, the Dons could have added some gloss to the scoreline, however sub Sam Nombe shot wildly over the top from inside the box when well placed.
It was a hard-earned victory for a Dons side that kept a good defensive shape throughout and despite having less chances than their opponents, converted their opportunity when it mattered to secure another Merit League success.
After the match, Edu Rubio said: “We have been working over the last couple of weeks on our defensive set-up.
“Normally we play very expansively but we have been conceding a lot of goals so we have been trying to compact and press high and today it worked.
“We managed to keep a clean sheet which is always good news so we achieved what we set up to do – we didn’t concede, we maintained our concentration and then we managed to create chances in the second half and score a winning goal.
“We never set up not to lose but we have been working on our defensive side and we wanted to be harder to beat.
“It is the first time we have played Cheltenham so at the start it was more about assessing the opposition and we did that and it was a good game.
“Ahead of the next game we will work on being solid at the back, being hard to beat and then being clinical with taking our chances.”
Starting XI (4-2-3-1): Jones; Kasumu, Omar, Tapp, Evans (Kioso 66); Bonsu (Osei-Bonsu 75), Wright (Freeman 84); Asonganyi (Nombe 55), Logan (c), Bell; Thomas-Asante.
Goal: Omar (88)
Booked: Bonsu, Evans