The win saw the Whites claim a much-needed three points following back-to-back defeats to Huddersfield and Hereford.
Jonathan Douglas and Andy Robinson both hit the woodwork before Cheltenham goalkeeper Scott Brown defied Leeds with a string of fine saves.
Howson broke the deadlock after 54 minutes when he headed in Robinson's right-wing cross before doubling United's advantage 11 minutes later.
The midfielder took Fabian Delph's pass before shooting past Brown as Leeds recorded their fourth successive home win.
At the other end Casper Ankergren had little to do in the Leeds goal as Cheltenham offered little in attack. But the goalkeeper was on hand to make a blocking save to foil Lloyd Owusu shortly before the break.