Connor Brown was given a controversial red card just before the half time break after a challenge on Kyle Reid.
That affected the flow of Latics and on 50 minutes, McMahon looped a header over Joel Coleman to win the game for the Bantams, denying Sheridan a winning return as manager.
The new manager opted to bring defender James Wilson back into the starting 11 as he lined up in 5-3-2 formation at the start of the game.
Latics almost got off to a disastrous start as Bradford’s Rory McArdle struck inches over Joel Coleman’s goal from 12 yards.
Sheridan’s men started to settle into the game and a strong run from Winchester saw him progress over 50 yards but his final pass just could not find Jake Cassidy.
The home side had pace in their side through Reid, but his final delivery let him down.
He dragged a shot wide on 15 minutes as the game started to heat up.
Lee Evans was lucky to escape without a booking after a late challenge on Liam Kelly whilst a minute later, McMahon saw yellow for a similar challenge on James Wilson.
That made referee Ben Toner unpopular with the home supporters, and soon he would become public enemy number one with Oldham supporters.
Cameron Dummigan was replaced by Brown on 24 minutes after the Burnley loanee picked up an injury.
It was mainly a midfield battle, with both sides struggling to create clear cut chances on goal.
Whilst Reid blazed over from the edge of the box, Latics had their best opportunity of the half five minutes before the break.
Mike Jones’ cross was turned into the path of Cassidy who flicked a boot at the ball and it looked to be past the goalkeeper. Ben Williams, however, managed to claw the ball off the line and away from danger to the disappointment of Latics.
A minute later came the controversial point of the game. Brown, who had been on the field for 16 minutes, received his marching orders for an apparent late challenge on Kyle Reid.
The two came together in the middle of the park and the referee adjudged Brown to have caught Reid with his boot and dismissed the full back.
The decision split opinions in the press box, however, the Oldham supporters voiced their anger at the referee.
With Latics needing to go into the break quickly to regroup, Bradford almost took the lead into added on time in the first half.
Hanson was presented with space in the area but out of nowhere, Timothee Dieng blocked the shot to keep the scores level at the end of the first half.
Five minutes into the second half, however, it was the home side who took the lead through McMahon.
James Meredith’s cross to the back post found the head of the right winger, and it looped over Coleman and into the back of the goal.
That goal seemed to kick Latics into life and Jones was presented with a chance from 25 yards but his free kick rebounded against the wall.
From the follow up, however, he drove just wide of Williams’ post as Latics pressed for an equaliser.
Bradford almost doubled their lead two minutes later as a poor clearance from Coleman was picked up by Christopher Routis but the midfielder hit it inches over the crossbar.
On the hour mark, a superb one-two move down the left between Mike Jones and Danny Lafferty saw the ball fall to Winchester on the edge of the box but his goalwards shot was blocked.
Bradford started to make their man advantage count as they took control of the game but on the break, Latics looked threatening.
Firstly for the Bantams, Billy Clarke blazed over the crossbar from distance and then Hanson headed over a McMahon cross into the box.
Both managers made changes and Sheridan brought on Dominic Poleon and Jonathan Forte to add attacking flair.
With 10 minutes remaining, Jones found Brian Wilson at the back post but his cross was just headed away from danger.
Despite the man advantage, Bradford were doing their best to waste time and slow the game down, evident when Meredith was booked for time wasting.
The supporters felt Latics should have been awarded a penalty on 87 minutes after Nathan Clarke looked to handle in the area but the referee waved away the protests.
Into additional time and Athletic and Forte believed his should have been awarded a penalty. The ball flicked up onto the hand of a Bradford defender and again the referee said no.
Latics had one more chance before the end of the game as Kelly forced Williams into smart save at the back post and Sheridan’s first game ended in defeat.
Bradford City: Williams, Darby, McArdle, N Clarke, Meredith, McMahon, Routis (Marshall 80’), Evans, Reid (Morris 61’), B Clarke (Cole 63’), Hanson
Subs not used: Cracknell, Knott, Leigh, James.
Oldham Athletic: Coleman, Dummigan (Brown 25’), Dieng, J.Wilson, B.Wilson, Lafferty, Kelly, Jones, Winchester (Forte 63’), Murphy (Poleon 66’), Cassidy.
Subs not used: Cornell, Mills, Croft, Fuller.
Goals: Bradford City (McMahon 50’) 1-0 Oldham Athletic
Attendance: 18,522 (992 visiting supporters)