Wilson's side kept their fifth consecutive clean sheet as they attempt to make up for last season's play-off heartbreak by securing a top-two finish. Struggling Oldham gave them a tough battle, but United almost grabbed a first-half lead when Harry Maguire was denied by keeper Alex Cisak.
The breakthrough came in the 57th minute as Cisak could only parry Dominic Poleon's angled shot, giving Michael Doyle the chance to tuck in the rebound from 12 yards. Oldham's fate was sealed four minutes from time when Cisak charged off his line, failed to gather Tony McMahon's free-kick and allowed Dave Kitson to head into the empty net.
Blades boss Wilson said: "It's a great win and you could see how much it meant to everybody. To go five games without conceding is excellent and it's down to the whole team's efforts, not just the defenders.
"Different teams offer different problems and Oldham caused us an extreme problem with their physicality. We all saw the problems Matt Smith gave Everton in the FA Cup, plus they have big centre-halves and they brought on Chris Iwelumo.
"Our defenders were enormous and didn't budge an inch, which was important because the more you back off the more difficulties you will have. We kept Oldham out of our box for a lot of the game and we worked very hard from front to back.
"We have the quality to score goals at the other end, but our defensive record is making a big difference. There will be twists at some point, but we'll set out our stall to win every game from now to the end of the season."
Oldham's defeat, which ended a run of three straight league wins under caretaker manager Tony Philliskirk, plunged them back into npower League One's relegation zone.
Philliskirk said: "There wasn't a lot between the sides, but we made two individual mistakes and got punished both times. It's disappointing, but we had a real go and we should have had an unbelievably blatant penalty for a push on Robbie Simpson. It isn't nice being back in the bottom four, but we already knew we had some massive games ahead of us and that we needed points as quickly as possible.
"It isn't panic stations and there were positives to take from a very difficult game against a very good side. I've seen a lot of Sheffield United this season and they are the most efficient side in League One - I'll be absolutely gobsmacked if they don't go up."