United battled back from a 2-0 half-time deficit to claim what could be a vital point in the push to secure a play-off berth.
Former Lane loanee Dominic Poleon scored both goals for Oldham - including an impressive second - before Scots duo Jason Holt and Jamie Murphy earned United a point.
In fact it could have been more for the Blades, who dominated the second half, Michael Doyle was denied by a fingertip save and a post.
Clough attempted to freshen up his team for the third fixture of the week. Kennedy, Reed, Doyle, Murphy and McNulty all started. Harris did not recover from his midweek injury, whilst Baxter, Coutts, Done and Steven Davies dropped to the bench.
In a fast and furious start in sunny, but windy conditions, a backpass by Basham put Howard under pressure early on and the goalkeeper's clearance struck Philliskirk and trickled wide. The Blades goalkeeper also had to be alert to hold a long-range Kelly shot on nine minutes, which did not take a true bounce in the sandy goalmouth.
Oldham settled the quicker and former Blade Philliskirk saw a lot of the ball. United's first chances saw Flynn struggling with an injury as he tried to get on the end of Holt's through ball and then McNulty was put in the clear on 21 minutes but his shot was straight at goalkeeper Coleman.
An error of judgement from Kennedy then gave the home side the chance to open the scoring at the midway point of the half. It left Basham to deal with the advancing Philliskirk, who was used as a decoy, to enable POLEON to fire across Howard and into the corner of the net.
United's response was a couple of efforts from outside the box. Brayford had space but shot over and then Murphy's drilled effort was straight at Coleman. Reed was the first in the book for a foul on Philliskirk.
As half-time approached United put pressure on the home goal more but were stung by a second Oldham goal out of nowhere. On 43 minutes, the Blades had a couple of opportunities to clear before POLEON let fly with a 35-yard effort which was too quick for Howard, who was just a couple of yards off his line, but couldn't keep the ball out.
In injury-time at the end of the first half there was a chance to cut the deficit but from Brayford's shot, Holt was adjudged to be offside as he connected with the ball and before the break the diminutive Scottish midfielder also picked up a booking.
The start of the second half saw three substitutions, including two for the Blades - Scougall and Coutts replacing Kennedy and Reed - which meant positional changes for Brayford and Flynn. Poleon had an opportunity complete his hat-trick following a break from Turner, but the visitors made a better start.
After Freeman had been fouled by Kelly, Murphy's free-kick was on target but deflected off the wall before United reduced the arrears. Coutts, operating on the right, saw his cross beat two defenders and HOLT arrived at the right time to poke past Coleman.
Holt's close-range effort put the Oldham players and fans on edge for a spell but United weren't able to assert immediate follow-up pressure on the home goal. It took until 72 minutes when a neat move saw Doyle fire in a shot which would have rivalled Poleon's second but Coleman made a great save, flying through the air to tip over.
United's leveller, though, was just a minute away, albeit covered in controversy. The referee and one of his linesmen disagreed over whether a corner or goal-kick was the right decision but Mr Clark stuck to his decision and from Scougall's set-piece, Brayford and Basham both won headers before MURPHY forced the ball home in a crowded six-yard box.
The Blades were now dominating. McNulty was replaced by Davies and on 76 minutes another 30-yard from Doyle struck a post and rebounded to safety as Oldham breathed a sigh of relief.
United's substitutes had been used and Flynn and Murphy were carrying knocks but the visitors were still on top in the closing stages, a Coutts free-kick caused yet more problems for the home defence before they scrambled clear.
Four minutes of added time saw United waste a corner and a Blades wall had to repel a Jones free-kick, whilst there were a number of long throws and a corner before the referee was reminded to look at his watch, prompting him to blow the final whistle.
Oldham: Coleman, Brown, Mills (Sadler 45), Kelly, Jones, Poleon, Philliskirk (Murphy 81), Winchester, J. Wilson, Lockwood, Turner.
Unused: Mellis, Wilkinson, B. Wilson, Kusunga, Kean.
Blades: Howard, Brayford, Basham, Flynn, Doyle, Murphy, McNulty (S. Davies 75), Reed (Scougall 45), Freeman, Kennedy (Coutts 45), Holt.
Unused: Alcock, Baxter, Done, Turner.