Paul Green gave Latics the lead from the penalty spot midway through the second half and in the final 10 minutes Ryan McLaughlin rounded off the scoring to earn Sheridan his second win in charge.
Latics saw the game out professionally and the result takes them three points away from safety and saw them record their second home clean sheet in a row.
Sheridan made four changes to his side which lost to Shrewsbury Town at the weekend.
Aaron Holloway came back for his second debut for the club and made a nuisance of himself in attack, winning headers and flick ons.
It took the game a while to get started but it would be Latics who had the better chances in the first half.
Ollie Banks hit an effort over the crossbar from 25 yards on nine minutes whilst two minutes later his free kick was deflected wide of the goal from the edge of the box.
Latics were knocking on the door of the opening goal and striker for the night Ryan McLaughlin was the next to go close on 19 minutes.
The 22-year-old held the ball up in the penalty area, turned in the box but his shot took a deflection and went inches past the post.
The game turned into a midfield battle as Latics struggled to keep hold of the ball in dangerous areas.
Captain Peter Clarke was a threat in the air from set pieces and on 37 minutes almost netted the opening goal of the night.
After Banks’ free kick was partially cleared, McLaughlin hooked the ball back into the box but Clarke’s effort on the volley went over the crossbar.
Holloway was booked five minutes before the break whilst the visitors had a chance on the stroke of half time but Tom Nichols effort went wide of Connor Ripley’s far post.
Latics started the second half strongly and really took the game to their opponents.
Paul Green had the first effort of the second half but his volley was well handled by Posh goalkeeper Luke McGee.
A minute later, McLaughlin’s bursting run saw him strike from the edge of the box but again McGee made the save.
Clarke saw a header cleared off the line on 51 minutes after a corner from Banks as Latics continued to take the game to Posh.
Latics fans felt a penalty should have been awarded from the following corner as Gerrard went over in the box but the referee waved away the protests.
Sheridan’s side continued to throw balls into the box and upset the Peterborough United defence.
And that persistence would pay off on 68 minutes as the referee awarded Athletic a penalty for hauling down a player in the penalty box.
Green stepped up and sent McGee the wrong way as SportsDirect.com
Park erupted with noise and Latics went a goal up.
Athletic continued to put the pressure on Posh as Banks’ long corner found Holloway at the back post but the striker smashed over from 12 yards.
Flynn, who had an impressive game, was booked on 77 minutes but five minutes later he set up Banks who forced a good saved from McGee in the Posh goal.
However, a minute later, McLaughlin added the second goal of the game to seal the victory.
It was superb hold up play from Holloway to set up the goal, he crossed into the centre for McLaughlin and the winger could not miss from five yards.
Latics saw the game out confidently and professionally despite Marcus Maddison striking the crossbar from 30 yards in the final minute.
A huge crowd of 7,224 witnessed the victory as Latics marched on and picked up three vital points.
Oldham Athletic: Ripley, Wilson, Gerrard, Clarke, Reckord, Fane, Banks, Green, Flynn, McLaughlin (Mckay 88’), Holloway (Ngoo 89’).
Subs not used: Kettings, Law, Edmundson, Mantack, Erwin.
Peterborough United: McGee, Smith, Hughes, Bostwick, Tafazolli, Edwards (Da Silva Lopes 59’), Forrester, Angol (Taylor 59’), Maddison, Ball, Nichols (Morias 73’).
Subs not used: Tyler, Inman, Binnom-Williams, Samuelson.
Goals: Oldham Athletic (Green 69’, McLaughlin 82’) 2-0 Peterborough United
Attendance: 7,224 (442 visiting supporters)