Neil Danns had opened the scoring from close range in the closing stages of the first half for Palace, but Becchio`s headed equaliser in the 81st minute was followed by a well-taken second moments later as the Whites stretched their unbeaten run to seven games.
The home side were hit by a superb counter-attacking goal before the break. Nathaniel Clyne did well to get to the byline and get the ball across. It was behind James Vaughan but reached Danns at the far post and he side-footed home his fourth goal of the season.
Leeds finally got the goal they deserved with nine minutes remaining. Neil Kilkenny`s corner was flicked on by George McCartney and then Billy Paynter, and Becchio was on hand to get the final touch over the line.
And the same player snatched a second shortly afterwards, collecting the loose ball and holding off the challenge of a defender before slotting the ball past Julian Speroni.