Alex MacDonald scored the first goal of his loan spell from Burnley and Robbie Weir struck twice with headers as the Brewers moved back into the automatic promotion places.
Rowett was delighted with the outcome after a slip-up by his side against Bristol Rovers last time out.
The Burton boss said: "The defeat at Bristol Rovers was a disappointment and I just wanted us to come back strong and do ourselves justice again.
"I thought we did that comprehensively - and to get nine home wins in a row is a fantastic achievement.
"We still need to work hard at improving our away form to give ourselves an even better chance of promotion.
"But I think we've showed against a really strong Cheltenham side that we've got a squad as good as any in this league.
"We worked on things during the week to exploit one or two weaknesses - and that included getting the ball into their box from wide positions.
"I that thought Alex showed a lot of quality in that respect and Robbie got the goals he's been threatening in recent games."