Prolific young Irish striker Ronan Hale netted the only goal on the half-hour mark with a neat finish at the near post, following Kyle McFarlane's surging run.
With several players in action elsewhere with the First Team, Development Squad Coach Richard Beale put a youthful side out against the Brakes.
But they more than matched their more experienced non-league opponents
"Leamington are a very big and strong side that play a very direct game and rely heavily on set-pieces," said Beale.
"That was why we took the game, because it's good for the young players to be exposed to more football like that, which is the real game.
"We managed to keep a clean sheet by scrapping and putting our bodies on the line and that is often more important than the tactical side of it.
"It's an area where I think we need to become stronger because at the minute with the group of players we've got it doesn't come naturally to them, so that's a big of focus of the work we'll be doing this season."
Beale continued: "I thought we moved the ball about quite well on a sticky pitch and when we got it we broke quickly.
"These are the sorts of things we have been doing in training - breaking at pace, and that was where the goal stemmed from."