Jermaine McGlashan's phenomenal strike was the highlight as Cheltenham overcame fellow promotion chasers Rotherham to move up to fourth.
The Millers saw Lee Frecklington's early shot tipped over by Scott Brown, but from then on it was one-way traffic in the hosts' favour.
McGlashan's first-time volley flew in to put the Robins ahead, before Marlon Pack's effort from the edge of the box.
Steve Elliott stroked in a third after a blunder from keeper Andy Warrington.
Warrington dropped an 84th-minute corner to allow Elliott an easy finish and help his side move to within two points of the League Two automatic promotion places.
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Cheltenham Town Manager Mark Yates told BBC Radio Gloucestershire:
"From start to finish we dominated, and more than matched their effort, passion and commitment, and could and should have scored more.
"We were aggressive and set an early tempo and I thought that was the key to the win.
"Today was about matching what they're good at, and it was really good to score a few and keep a clean sheet.
"This win was for Jason Taylor today, although he wasn't able to play today he made sure that the players were up for the game."
Rotherham United manager Steve Evans told BBC Radio Sheffield:
"We've not turned up have we? First half we had a lot of good possession but done nothing with it.
"We didn't have any penetration in the final third.
"I think everyone of their [three] goals today were because of individual errors.
"And when you make big individual errors your going to concede goals."