Becchio was left with a 53rd minute tap-in when Jermaine Beckford cut in from the left and his shot was parried by Dean Brill straight to the Argentine.
Seven minutes later Jonny Howson made inroads on the right and Becchio rose to head in a pinpoint cross by the industrious Robert Snodgrass.
Leeds had two penalty claims against central defender Reuben Hazell rejected by referee Paul Taylor.
First Hazell fell over Beckford inside the penalty box with 17 minutes gone. Then, a minute before the break, Becchio stumbled to Hazell's clumsy challenge as the Argentine was played in by Snodgrass.
Hazell and former Leeds defender Sean Gregan gave impressive performances at the back for Oldham and Hazell was perfectly positioned to clear a shot from Andrew Hughes off the line in first-half injury-time, but neither were able to stop Becchio in the second period.