Grayson's club jumped above Millwall into second place and closed in on leaders Norwich as Beckford's replacement, Becchio, struck either side of fellow front-runner Max Gradel's flashing header to secure a comfortable victory over Carlisle United that invigorated the push for the Championship.
Related ArticlesBeckford transfer saga 'unsettled Leeds'Leeds' fall, rise and fall againLeeds players 'must raise their game'League One tableLeague One fixturesSport on televisionThe former League One pacesetters rediscovered their old verve from the outset, starting vibrantly as 27-goal leading scorer Beckford stewed on the substitutes' bench and a chance came and went for Gradel before Becchio struck.
He was first to react when goalkeeper Adam Collin surprisingly spilled Robert Snodgrass' curling 25-free-kick in the 13th minute and the Argentine forward slotted the ball in from close range.
Becchio went close from distance before wasting a glorious opportunity following Snodgrass' cross but got became disorientated and knocked the ball wide with the goal at his mercy.
Former Leeds defender, Ian Harte, inadvertently aided his old club's cause when he nodded the ball straight to Gradel but Collin repelled his close-range volley with his legs on the half-hour.
Grayson was left to rue Gradel's lack of a finishing touch in the 43rd minute as Leeds lost their composure and right-back Richard Keogh stooped to nod Harte's free-kick past the impressive Shane Higgs after Naylor recklessly fouled Gary Madine.
Beckford might have been expecting to get the nod at half-time but Grayson stuck with Gradel who repaid his faith when he rose above Carlisle's defence to powerfully head in Leigh Bromby's cross two minutes after the break.
Becchio doubled the lead three minutes later when he raced clear before confidently tucking away a low left-footed shot beneath Collin for his 15th goal this term following Gradel's through-ball before Beckford entered the fray late as â What a waste of money' taunts echoed around Brunton Park.
Carlisle (4-4-2): Collin; Keogh, Aldred (Raven 64), Harte, Horwood; Dobie (Bowman 81), Thirlwell (Bridge-Wilkinson 60), Taiwo, Marshall; Madine, ClaytonSubs: Pidgeley (g), Kavanagh, Rothery, Kane.Booked: Clayton Goal: Keogh 43 Leeds (4-4-2): Higgs; Bromby, Naylor, Collins, Hughes; Howson, Kilkenny, Doyle, Snodgrass; Gradel (Grella 88), Becchio (Beckford 88). Subs: Ankergren (g), McSheffrey, Parker, Lowry, Watt Booked: Naylor Goals: Becchio 13, 50 Gradel 47 Referee: M Halsey (Lancashire)