Leeds made two changes from the side beaten in midweek, Andy Hughes replaced Carl Dickinson and Jonathan Douglas replaced Lee Trundle with Robert Snodgrass moving into a more forward role.
Leeds quickly went about trying to put Tuesday`s woeful performance behind them and Becchio had an early chance but just failed to reach a Howson cross.
The Whites dominated the early exchanges and Douglas and Delph both went close.
Douglas went even closer on the half hour but his header came back off the bar.
Brown in the Cheltenham goal then made good saves to deny Howson and Snodgrass.
Leeds really should have been in the lead with chances being squandered on a regular basis, Kilkenny who had just replaced Hughes through injury failed to shoot when in a great position.
Robinson then rattled the Cheltenham woodwork for a second time when his header hit the post.
Leeds who had rarely been troubled then had a stroke of luck when Owusu was in a great position for the visitors but he shot straight at Ankergren.
Robinson then had a good chance to score for Leeds just before half time but his free kick went wide of the post.
Leeds continued the second half much the same way the first had finished, Kilkenny and Delph both going close with efforts.
They finally broke the deadlock when Howson headed in from a Snodgrass cross.
Cheltenham soon thought they had equalised when Owusu had it in the Leeds goal but the assistant had raised his flag for offside.
Howson got his second of the afternoon after being put through by Becchio and his left foot shot beat the Cheltenham keeper.
Snodgrass had Leeds next chance when his free kick was saved by Brown.
Kilkenny and Trundle had chances to increase Leeds lead has they strolled towards three points.
A good performance from Leeds and with many results going in their favour they are right back in the play off picture.
Leeds United – Ankergren, Marques, Naylor, Parker, Hughes, Howson, Delph, Douglas, Robinson, Becchio, Snodgrass
Substitutes – Lucas, Michalik, Kilkenny, Grella, Trundle
Cheltenham Town – Brown, Townsend, Wright, Westwood, Diallo, Westlake, Russell, Finnigan, Antonio, Owusu, Bignall
Substitutes – Puddy, Watkins, Bird, Spencer, Hammond
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