Adrian Forbes’ side were 5-0 to the good at half-time and led as early as the second minute when Jayden Luker – who was on the bench for the senior side’s Premier League game at Aston Villa on Sunday – bent a wonderful strike into the top corner.
The Town doubled their lead on 16 minutes when Jake Burger calmly dispatched a penalty after Millar Matthews-Lewis had been tripped in the box.
Two turned to three five minutes later when Axel Piesold slid home unmarked and barely 60 seconds had elapsed when Oli Lynch tapped home to make it 4-0.
The goals kept coming, and shortly after the half-hour mark Burger rolled the ball home after latching onto Matthews-Lewis' through ball.
It took the Town just two minutes into the second half to score their sixth of the evening when fine work from Luker teed up Oli Lynch to fire home from close range.
Marcus Daws replaced Matthews-Lewis in Forbes’ first change of the night on 71 minutes and seven minutes after his introduction, the attacker finished Burger’s pass to make it 7-0.
Another substitute, Sam Anderson, completed the scoring with eight minutes remaining with his first touch having taken Daws’ pass.
After losing last week in a friendly against Notts County, Forbes was delighted to see his side return to winning form.
“That was a better performance from the boys – the application, attitude and work-rate was superb from the outset,” said the Town coach.
“A fantastic early goal from Jayden settled everything down and after that we were comfortable.
“We passed and moved the ball well with tempo and intensity and that made it really difficult for Kempston.
“From my point of view, it was important that we found a way to get back to winning ways, especially with our next Premier League Cup game against Colchester coming up.
“The boys were in a lose-lose situation tonight. Lose, and questions would have been asked; while on the other hand they were expected to win, so they handled it really well.
“However, the most important thing is that we’re through to the next round where we will make sure we have another positive performance again.”
Town: Trialist A, Chigozie, Luker (sub Emery 83), Piesold, Pinnington, Kayibanda, Phillips, Nelson, Lynch (sub Anderson 77), Burger, Matthews-Lewis (sub Daws 71).
Subs not used: Hockey, Lorentzen-Jones.