Latics made it back-to-back away wins thanks to three goals and a Magnus Norman penalty save at The Hive.
Oldham got off to a great start when Ellis Chapman found Mark Kitching at the near post with a corner, as Kitch flicked the ball towards goal and past Azaze.
The hosts equalised shortly before the half-time whistle, Harry Pritchard’s cross found Idris Kanu at the far-post, who tapped in from a few yards out.
Unsworth’s side retook the lead when Mike Fondop latched onto a loose ball, and fired home from a tight angle.
The Bees pressed for another equaliser, and won a penalty through an apparent handball, but Norman made a fantastic save to keep Latics in the lead.
Peter Clarke secured the three points when he volleyed home from a corner in stoppage time.
Latics started the game brightly, and won a corner for their early attacking efforts.
In a move straight from the training ground, Chapman crossed the ball to the unmarked Kitching at the near post, who slotted the ball past the ‘keeper.
Both sides exchanged passes for a good chunk of the first-half, Kanu had a chance to equalise with a volley from inside the area, and Latics could have doubled their lead from Nuttall’s glancing header, but neither could find the target.
The next goal did come from Barnet though, Pritchard’s cross was met by Kanu at the far post, who couldn’t miss from a few yards out, leaving the scores level going into the break.
Unsworth made a double change at half-time, Fondop and Reid came on in place of Nuttall and Chapman.
The substitutions showed clear attacking intent, and that paid off with a series of good chances during the opening periods of the second-half.
John Rooney swung in a free-kick toward Fondop who could only aim his header straight at Azaze.
Fondop would get his goal, however, Reid was clattered by the ‘keeper, with going down and the Barnet defence coming to a standstill. Fondop didn’t though, and he ran onto the loose ball and found the net from the side of the penalty area.
Potter fired a magical header towards goal, and looked certain to score, but Liam Hogan was able to get his own head on it and clear the ball off the line.
Fondop thought he’d got a second when he tapped home at the far post, but the linesman raised his flag for offside.
It looked as though all of Oldham’s great work would be undone when the Bees won a penalty with 15 minutes to play.
Set-piece expert Gorman was tasked with beating penalty-saving expert Norman, and it was Norman who got down well to make another great save from a penalty.
Barnet threw the kitchen sink at the Athletic defence, seeing a number of shots blocked and saved, but none made their way past Norman.
With the hosts so vulnerable at the back, P. Clarke secured the points with a terrific volley from a Rooney corner.
Latics: Norman, Hogan, Sheron, Green (P. Clarke 73), Shelton, Rooney, Kitching, Sutton, Chapman (Fondop 45), Yarney, Nuttall (Reid 45).
Subs not used: Hudson, Tollitt.
Attendance: 1,299 (167)
Referee: Jamie O'Connor