The 21-year-old struck the first goals of his career in the final 20 minutes after Burton had trailed to a Byron Harrison effort - extending the Brewers' unbeaten run to 11 matches.
Scott Brown had to tip over a header from defender Zander Diamond as Burton made the early running.
The visitors could have gone in front in the 37th minute but Jermaine McGlashan fired over a gaping net from eight yards after being found by Sam Deering's throughball.
Burton quickly had another chance of their own but Brown produced a leaping save to keep out a Billy Kee header, before the goalkeeper's efforts were matched by opposite number Dean Lyness to deny Harrison.
The visitors' improved play was rewarded in the 62nd minute when Jason Taylor muscled his way through to make an opening which was tucked away by Harrison from 12 yards.
Cheltenham had an amazing escape when Kee's shot hit the inside of both posts but stayed out.
But Burton's substitutions paid off when Knowles stabbed in Zeli Ismail's cross in the 71st minute.
And the move was repeated five minutes from time as Knowles fired home another Ismail cross to clinch all three points for Gary Rowett's side.