The game was one of only two to go ahead in League Two and Northampton took full advantage to edge nearer to the play-offs as substitute Jake Robinson and Clive Platt grabbed second-half goals in a 2-0 victory.
Cobblers laid seige to the Aldershot goal from the start but the visitors withstood the early barrage.
Robinson broke the deadlock four minutes after coming on at half-time and Platt made the game safe deep into stoppage-time. In between, Danny Hylton missed a great chance to equalise and Dani Lopez was denied by Cobblers goalkeeper Lee Nicholls.
"The groundstaff produced a fantastic effort to get the game on so it was important we did our job on the pitch," said Boothroyd. "It was a good old fashioned English game and we had to work really hard to get the result. We've got to improve in certain areas but I thought we were well worth our win and got what we deserved.
"We needed more width and that's why I brought Jake Robinson on, to stretch their defence and make Clive Platt more effective. Sometimes it works, sometimes it doesn't, but it did in this game.
"Clive is a Championship player playing in League Two and he's a quality player, so I'm delighted he came here and got on the scoresheet. Jake Robinson went out on loan but has really picked his game up since he's returned and I was very satisfied with his second-half performance."
Aldershot boss Dean Holdsworth was left to reflect on what might have been. He said: "I'm partly disappointed but also very pleased with the way we played.
"We created more one-on-one situations than we have all season but we have to be more clinical. We're usually very good in front of goal but not here, which is unlike us.
"Dani Lopez and Danny Hylton had a couple of one-on-one's and they usually put those away and that was what was missing."