Glenn Murray denied Leeds a clean sheet by scoring two minutes into added time but the Seagulls were well beaten.
Leeds' Paul Telfer was ruled out with a groin strain but Brighton's leading scorer Murray passed a late fitness test on his thigh.
Leeds fans made Brighton's on-loan midfielder Robbie Savage a constant target for their jeers and the Welsh international directed a couple of gestures towards them as he ran over to take a corner, the officials presumably failing to notice.
The Seagulls, without a win at Elland Road since 1985, had plenty of possession, but caused Leeds keeper David Lucas little trouble and there were first-half bookings for Dave Livermore and Colin Hawkins for over-robust tackles and Tommy Elphick for tugging Beckford's shirt.
Referee Carl Boyeson had further words with Livermore and his captain Steve Thomson and Brighton almost fell behind after 24 minutes when Rui Marques played a long ball forward for Beckford, who prodded a first-time effort narrowly wide of the near post.
Frazer Richardson troubled Michel Kuipers with a couple of stinging drives before Leeds scored twice in as many minutes just before the break.
Becchio opened the scoring with his fifth goal of the season in the 45th minute. Richardson and Andrew Hughes did the spadework and although Becchio's first shot from eight yards was blocked, the Argentinian's second billowed the net.
In the second minute of time added on, Aidan White made a long run down the left and Fabian Delph's deep cross was superbly headed home by the leaping Beckford for his 12th goal of the season.
Hawkins and Livermore made way for Dean Cox and Kevin Thornton at the start of the second half but Leeds almost made it three when Marques headed Neil Kilkenny's corner against the bar.
Beckford spurned a clear chance created by Becchio and Delph went close from 25 yards, before players on both sides had to be separated during a 76th minute flare-up in what had been an ill-tempered match.
Beckford drilled his second goal when played through by Delph, before a late defensive slip-up by Leeds enabled Murray to stab the ball past Lucas.