Becchio headed in his 13th goal of the season from a Robert Snodgrass corner just one minute after Oldham had gone in front.
Leeds had lost three consecutive away games without finding the net but they shaded a tense first half, with Snodgrass and Jermaine Beckford squandering chances.
The Latics, wearing pink to raise awareness for a breast cancer charity, broke through six minutes after the break when Lee Hughes seized on a loose ball and somehow volleyed past goalkeeper Casper Ankergren from an acute angle.
But Leeds came storming back and Becchio was thwarted by Greg Fleming's tremendous save, but Becchio levelled from the resulting corner when he was left unmarked six yards out and headed home off the crossbar.
Both sides pushed for victory but Leeds had the clearest opening after a fluent move cut through Oldham's back four. Fabian Delph tried to thread his shot into the far corner, only for Fleming to deny him at full stretch.