The visitors were well worth their victory and took a stranglehold on the game after just 15 minutes when Orient defender Tamika Mkandawire handled and Bradley Johnson whipped in a free-kick that defender Huntington knocked past Orient keeper Glenn Morris from close-range.
Orient should have levelled five minutes later when Jason Demetriou and Adam Boyd linked and provided an opening for defender Mkandawire, but he crashed a volley over the bar from six yards.
But as Leeds continued to put their foot on the accelerator it was left to home goalkeeper Morris to keep the O's in the contest, as he made a great double save from Jonny Howson and Dougie Freedman just past the 30-minute mark.
Orient did finally find a semblance of form and just before the break created two good chances.
First Boyd tested Leeds keeper Casper Ankergren with a dipping volley and then striker Jabo Ibehre headed wide following a cross from Demetriou.
But the home side were further hampered when they lost Alton Thelwell with a knee injury.
After the break Leeds quickly wrapped the game up with a killer second goal. Five minutes into the restart Orient defender Stephen Purches lost possession when he slipped over and Leeds launched a lightening break.
The ever dangerous Freedman provided the perfect cross and Beckford, from the edge of the area, fired home his 20th goal of the season.
Ten minutes later Beckford limped off injured and after that the visitors rarely threatened.
But although Orient came back into the game late on with plenty of possession they rarely troubled keeper Ankergren. The best efforts from the home side came from Charlie Daniels and Demetriou, as Leeds finished worthy winners.