A flowing three-man move down the right resulted in John Spicer pulling the ball back from the by-line only to see Andy Gray fire the ball over the cross-bar.
Oldham were forced to make a change when Deane Smalley picked up a knock following a challenge by Steve Jones and was replaced by Andy Liddell.
Liddell was soon involved in the action, but wasted a good opportunity by firing wide of the target.
Oldham's best opportunity of the first half came after 33 minutes when the home team failed to clear a corner and Gary McDonald shot through a crowd of players only to miss the target by inches.
Perhaps frustrated by his side's efforts, Clarets manager Steve Cotterill made a double substitution at half-time with James O'Connor and Alan Mahon replacing Joey Gudjonsson and Steve Jones.
Robbie Blake came close to breaking the deadlock with a ferocious free-kick from 25 yards which struck the foot of a post with keeper Mark Crossley well beaten. Whilst at the other end Latics striker Craig Davies was denied by Brian Jensen.
The home side went in front on the hour mark as McDonald lost possession to Gray and his shot looped over stranded keeper Crossley.
A fine piece of individual skill by Davies forced Jensen to produce a good save and prevent an equaliser for the Latics.
Jensen was again called upon to make a fine save from Chris Taylor, while Wade Elliott missed a glorious opportunity to kill off the visitors but fired wide.
However, Oldham's respite was brief as Blake latched on to a defence-splitting defence from Alan Mahon to fire past Crossley.
But still Oldham kept pressing forward and McDonald's evening was summed up when his goal-bound shot was deflected for a corner by Clarke Carlisle.
To rub salt into Oldham's wounds Elliott sent substitute Akinbiyi clear and the striker scored with the last kick of the game.