Josh Low headed the Robins in front after a goalless first half and James Spencer sealed their win with his fifth of the season.
The Robins had the first opportunities to break the stalemate in a flurry of pressure midway through the first half.
Defender Steve Elliott had a fierce shot charged to safety and from the corner that followed, Sido Jombati's header was kept out by a reaction save from Ross Atkins.
After struggling for form, Burton had an even better chance in the 37th minute when Cleveland Taylor's cross found Justin Richards unmarked but the striker fired into the body of Jack Butland in the Cheltenham goal.
The Robins grabbed the lead two minutes after the break as Low charged unmarked onto a Luke Garbutt cross to power a six-yard header into the roof of the net. The visitors doubled their lead in the 65th minute as Kaid Mohamed finished a strong run on he left with a precision cross that was converted by Spencer from close range.
A dominant first half saw Port Vale cruise to a 3-0 victory over Northampton.
The hosts scored three goals inside the opening 26 minutes as they recorded a first triumph over the Cobblers in seven meetings.
Vale were bidding to set a new club record of scoring in the first 16 games of a season and woeful defending enabled them to do so as early as the fifth minute. The Northampton rearguard stood like statues as Doug Loft's corner bounced into the path of Tom Pope who headed in unchallenged from four yards.
Anthony Griffith rifled in the second with a 35-yard shot in the 20th minute which went in despite Sam Walker getting a hand to it. And a rout was on the cards when the persistent Pope headed forward to set up big defender John McCombe to prod in Vale's third from close range six minutes later.
Northampton stemmed the tide for the rest of the first half, but their dismal night was summed up three minutes after the interval when Lewis Young fired over a gaping net.
Cobblers centre-back Kelvin Langmead went closest to a consolation goal when he struck a post eight minutes from time, but Vale coasted to a victory which lifted them to fifth place in the table.
Bristol Rovers fought off a Rotherham fightback to win 5-2, after leading 3-0 at one stage.
Rotherham, who also had a player dismissed, fought back to 3-2 but Rovers went on to complete an emphatic win.
Scott McGleish scored twice for Rovers, the second a penalty, and their other goals came from Cian Bolger, Lee Brown and Joe Anyinsah.
Rotherham's goals came from Jason Taylor and Danny Schofield but they ended the game with 10 men after Guy Branston was sent off with the score 3-2.