Argentinian Becchio was a source of constant frustration to the home defence and smashed in his fourth goal of the season after half an hour. Neil Kilkenny's deep corner looked to be heading out of play before veteran Paul Telfer stretched to knock the ball back to Becchio, who made no mistake from ten yards to clip a volley into the roof of the net via the head of defender Evan Horwood.
It was hard to take for Carlisle who had imposed themselves on the visitors in the opening exchanges and were unlucky when Simon Hackney's mis-hit cross ran along the length of the crossbar early on. Winger Hackney had his marker Frazer Richardson tied in knots and was the only true threat to Leeds keeper David Lucas.
Danny Carlton and Paul Thirlwell both tried their luck from distance before Cleveland Taylor headed over when well placed. Hackney again ran rings round the Leeds defence in the second half and his pinpoint cross was headed agonisingly wide by substitute Scott Dobie after 64 minutes.
Sixty seconds later Lucas made a good block from Hackney's drive before Carlton's goalbound header was deflected over by Rui Marques. With the game now opening up Leeds captain Richardson cut inside onto his left foot to hit a stunning 30-yard drive that flicked off the top of the bar.
With eight minutes to play Hackney had his best chance yet, but after dribbling past Richardson his low drive took the merest of deflections to send the ball inches wide. As the hosts pushed forward desperate for a late equaliser Leeds hit back with a stunningly effective counter-attack.
Becchio robbed Thirlwell and poked the ball through for substitute Richard Snodgrass, who had plenty of time to pick out Beckford at the far post for his 11th goal of the campaign. The win for the visitors pushing them above Carlisle and into third place in the League One table.