United, with only one home win all season, looked set for a second after a blistering start in which they struck twice - and believed they had also got a third goal.
Brian Laws' side thought they had opened the scoring in the eighth minute when Jimmy Ryan crashed a header off the underside of the crossbar from a cross by Karl Hawley but the referee's assistant said the ball had not crossed the line.
Eight minutes later they were in front when a shot from Mark Duffy ricocheted around a crowded box and centre-back Niall Canavan scrambled the ball home from close range.
Three minutes later it was 2-0 when Duffy danced his way into the box from the left before drilling a shot into the bottom corner of the net past goalkeeper Dean Bouzanis.
Oldham reduced their arrears with their first real threat after 35 minutes when former Scunthorpe skipper Cliff Byrne netted from close range on his first return to Glanford Park after a good knock down at the far post by Matt Smith.
That was the turning point and the powerful Smith was always a threat up front for the visitors. It was a foul on him inside the box that won Oldham a 65th-minute penalty which Jose Baxter confidently converted for the equaliser.
Two minutes later there was more drama when the visitors were reduced to 10 men when midfielder James Wesolowski was sent off for his challenge on Damien Mozika.
But Oldham hung on to end a run of four successive defeats which had brought the axe for three of their backroom staff, including assistant boss Gerry Taggart.