Ben Harding grabbed the crucial goal in the 88th minute as the Cobblers made it seven wins on the bounce against an improving Rovers side at Sixfields.
Boothroyd said: "It was a scrappy game at times, especially in the first half.
"Rovers were full of running and it was two evenly matched teams going at each other. They are battling for their lives and we're going for promotion.
"In the end we managed to win it on a set-play but it doesn't matter when you win it, in the first minute or the last minute. It was a very tight game but we kept going to the end and the players were patient.
"The two most important things at this stage of the season are having all your players fit and making sure they are ready for the run-in and most importantly to keep going right to the end of games."