A quarter hour in Wanderers' Matt Phillips sprinted down the left wing and cut the ball back to Chris Zebroski in a great position but his soft finish was easily saved by Shane Higgs.
Moments later, Jermaine Beckford grazed the outside of Scott Shearer's post with a powerful strike after getting the wrong side of Luke Oliver.
Ten minutes before half-time Robert Snodgrass put Beckford in behind Wycombe again with a smart pass but the striker blazed well wide.
Leeds dominated after the break and after an hour Becchio slipped his marker Michael Duberry and found space to pick the ball up 25 yards out and smash it into the bottom corner.
United continued to control the game after taking the lead and came very close to a late second when Michael Doyle turned on the edge of the box and hit a powerful shot just wide.