A lively start to the game saw Andy Robinson have a shot blocked after a great bit of build up play.
Barnet were next to attack with United struggling to defend a corner kick. Becchio always looked most likely to open the scoring, first lifting a shot just over the bar then after some good work from Frazer Richardson, Barnet keeper Rob Beckwith pulled off a fantastic save from the Argentinian.
But Leeds took the lead on 36 minutes with a one man show from Andy Robinson.
The former Swansea man used his quick feet before firing an unstoppable shot from the edge of the box.
Minutes later Robinson almost set up Becchio to make it 2-0 but the trialist fired wide.
A lively opening to the second half saw Barnet with the first attack, Ismail Yakubu failing to convert a dangerous Kenny Gillet cross.
The second goal came soon after though for the Whites. A fine run down the middle of the park from Jonny Howson saw him pick his spot before he fired a wonderful shot the Barnet keeper had no chance of saving.
The home side tried their best to stay in the game, first Adomah testing Ankergren and then the lively Adam Birchill failing to convert a seemingly easy chance inside the six-yard box.
With just over an hour gone Gary McAllister decided to take another look at trialist Marcus Haber, bringing the Canadian on in place of the inneffective Showunmi.
Scott Gardner also replaced the impressive Becchio. The game settled down towards the end, although the Whites kept most of the possession.
Haber had a couple of chances, the first being crowded out after trying to finish off a Andrew Hughes effort, the second being deflected over.
Barnet tried to finish the game with a late goal of their own, but Cliff Akurang blasted well over the bar.
Leeds United: Ankergren, Richardson, Marques, Huntington, Sheehan, Hughes, Howson, Delph, Robinson, Showunmi, Becchio.
Subs used: Telfer, Michalik, Gardener, Haber.
Barnet: Beckwith, Gillet, Bishop, Yakubu, Leary, Adomah, Akurang, Birchall, Deverdics, Carew, Hart.
Subs used: Port, Medley, St Aimie, Tabiri, Kadoch, De Magalhaes.
Referee: M Russell