The Argentine netted his ninth and 10th goals of the season to settle the nerves of what had been an increasingly restless home crowd.
Athletic had battled manfully for almost an hour at Elland Road before Becchio's quickfire double handed the hosts a deserved victory.
Latics had almost endured the worst possible start when Jermaine Beckford fired narrowly wide of Dean Brill's left-hand post in the seventh minute.
With both teams desperately in need of three points, it was no surprise that the game was somewhat scrappy in the opening half-hour.
Pawel Abbott dragged Oldham's only real first-half chance wide, while at the other end, Latics cleared the danger when Brill failed to hold Robert Snodgrass' effort.
With Athletic struggling to impose themselves going forward, it was the home side who increasingly took control.
For all their possession though, Sean Gregan and Reuben Hazell were dominant at the heart of the Oldham defence.
Brill was out quickly to block Michael Doyle's close-range shot as the home supporters grew ever more frustrated with half-time approaching.
However, their nerves were eased eight minutes into the second half when Brill spilled Beckford's shot and Becchio tucked away the rebound.
The lead was soon doubled when Snodgrass tricked his way into the area and crossed for Becchio to head home from close range.
Chris Taylor forced Leeds keeper Casper Ankergren into his only serious save of the evening despite bringing Joe Colbeck, Tom Eaves and Kelvin Lomax off the bench.
It was Leeds who came nearer to scoring with Max Gradel hitting the sidenetting as Oldham were left to ponder Saturday's home game with league leaders Norwich City.