Ex-Oldham favourite Kilkenny burst into the six-yard box to bundle in Max Gradel's cross from the left on 37 minutes.
Leeds wasted several chances to increase their lead as Oldham keeper Darryl Flahavan had a fine game but Becchio sealed it eight minutes from time with his first goal since returning from injury.
Oldham could have made an early breakthrough when Dean Furman headed wide and they were a match for the table-topping visitors until Kilkenny tipped the balance.
Leeds, who left top scorer Jermaine Beckford on the bench, then made a string of openings only to be denied by Flahavan and poor finishing.
On-loan Sam Vokes could have bagged a hat-trick and the lively Gradel was denied after going clean through.
Oldham almost equalised midway through the second half when Paul Heffernan shot just off target but Leeds had their second when Gradel played an astute pass to Becchio, who finished neatly from 10 yards.