Goalkeepers Casper Ankergren and Mark Crossley were almost spectators in a goalless first half in which Paul Huntington and Robert Snodgrass spurned two heading chances for Leeds.
Huntington put no power behind his free header in the 32nd minute and former Livingston winger Snodgrass nodded just over the bar eight minutes from the interval after Oldham failed to clear Andy Robinson's corner.
Taylor was fortunate not to concede an own-goal when he headed just wide of Mark Crossley's left post and he spurned Oldham's only first-half chance, shooting straight at Ankergren.
However, he made amends with goals in the 50th and 65th minutes. First he was quickest to react with a close-range shot when Lee Hughes' header came back off the bar.
Then he drifted in from the left and curled the ball into the far corner to secure a 2-0 win.