The Blades gave a solid and competent performance to ensure that Danny Wilson celebrated his 100th game in charge with a win.
Second half goals from Michael Doyle and Dave Kitson were enough to beat Oldham on their own patch as the Blades chalked up a fifth clean sheet on the bounce.
A travelling contingent of 2,591 packed into the away end at Boundary Park and were singing at the final whistle as three more vital points were added to the tally.
There was no Higginbotham on the United teamsheet, Hill stepped up from the bench to take over at left-back and Whitehouse was added to the list of substitutes. Former Blade's apprentice Brown was named in the Oldham team.
Robson began in a central role but it was his strike partner, Kitson, who made the first impact, charging and causing problems for goalkeeper Cisak inside the first 60 seconds. Oldham's front two, Smith and Baxter, both had sights of goal, whilst for the visitors, Doyle's effort hit Robson and drifted wide.
In between a number of hefty challenges, the first committed by Croft, the goalscoring opportunities continued. Wesolowski and Simpson had efforts blocked after a period of nervous defending, whilst United's chances fell to defenders - McMahon curling a free-kick just wide, Collins having an effort kicked away and Maguire heading over a Robson corner.
Smith was appealing for a penalty in an aerial challenge but the offside flag had already been raised, whilst Baxter curled a free-kick over the crossbar after a couple of decisions went Oldham's way in quick succession.
Doyle followed M'Voto into the referee's book and before the break the Blades created two more chances, again falling to defenders. Maguire got on the end of a Robson free-kick but could not get enough purchase, allowing Cisak to turn the ball around the post, and McMahon linked up well with Flynn before the right-back's powerful shot was deflected over by Tarkowski. In first half injury-time, however, Oldham came very close to taking the lead but Baxter's shot from 20 yards was just over Long's crossbar.
A slow and messy start to the second half prevented either side from gaining any real momentum but as the sun began to shine on the Unitedites, a mistake was capitalised upon by the visitors.
With 57 minutes gone, Tarkowski dallied in possession and was robbed by Poleon, who cut in from the right and saw his shot blocked by the body of goalkeeper Cisak. But DOYLE raced onto the loose ball and found the target with a controlled effort, which found the target with the aid of a post.
Poleon's pace almost brought United a quick second when he got the better of Brown but the loanee's finish was rushed, whilst the home side's first chance of the second period arrived on the hour but Maguire kicked away Wesolowski's shot.
On 68 minutes there were big shouts for a penalty when Oldham fans believed Hill pushed Simpson away from Obita's cross, whilst the cramp suffered by Poleon, who was replaced by McFadzean, also appeared to upset the home supporters.
McDonald was booked for hauling back Baxter, whilst Oldham went close again when Smith's header from a Croft cross flew just past Long's left post on 75 minutes.
Oldham introduced more attacking power with Iwelumo coming off the bench but Smith's shot on the turn was pushed away by Long, who recovered to kick away the rebound. The Blades also had further chances, namely two Maguire headers, the second of which needed to be pushed away by Cisak.
The Blades sealed the points with moments remaining. McMahon delivered a free-kick from the halfway line and Cisak wandered off his line but was beaten in the air by KITSON who headed home from around 15 yards. The goalscorer celebrated with the Blades fans and was lost amongst them for a spell, earning himself a booking when he returned to the playing area.
Late on Long palmed away a Smith shot to protect his clean sheet and Doyle went close to make it three but his volley was parried away by Cisak but soon the final whistle was greeted with the sounds of 'one Danny Wilson' from the Blades fans who had made the trip across the Pennines.
Oldham: Cisak, Brown (Iwelumo 78), Grounds, Wesolowski (Obita 65), M'Voto, Tarkowski, Croft, Furman, Simpson, Smith, Baxter.
Unused: Iwelumo, Murray, Taylor, Millar, Jacob, Winchester.
Blades: Long, Maguire, Hill, Flynn, Doyle, McDonald, Kitson, Collins, Robson, Poleon (McFadzean 72), McMahon.
Unused: Westlake, Cresswell, Ironside, Whitehouse, Coyne, De Girolamo.