Lukas Akins, Tom Hamer and Hayden Carter put the hosts to the sword in the second half at the Keepmoat. Doncaster have now lost seven games in a worrying nine-game winless run.
Shot-stopper Ellery Balcombe had to be alert to keep out Joe Powell’s drilled effort.
The hosts’ first real chance of the game fell to Matt Smith as his powerful strike was deflected for a corner, before Fejiri Okenabirnie forced Ben Garratt into a good save.
Rovers went even closer as Tom Anderson’s point-blank cross was saved by Garratt.
Okenabirhie put the ball in the back of the net but Branden Horton was judged to have handled in the build up.
Butler’s boys were indebted to the woodwork as Tom Hamer’s header with the bar after beating Balcombe. But Burton came bursting out of the blocks after the break. Balcombe produced a super stop to keep out Akins’s effort from just six yards out.
But the striker made no mistake on the stroke of the hour as he fired the Brewers ahead from Ryan Edwards’s cut-back.
Jimmy Floyd Hasselbaink’s charges should have doubled their tally as Hamer, Edwards and Kane Hemmings all had efforts blocked.
And Doncaster were once again helped by the furniture as Edwards rattled the post before Hemmings fired the strike wide.
But Burton finally found their second with 16 minutes to go as Hamer blasted home from the edge of the box.
And Carter added gloss in the 78th minute with a simple finish.
Doncaster: Balcombe, Greaves, Wright, Anderson, Horton, Smith, Bostock (Richards, 69), Sims, Coppinger, Okenabirhie, Bogle. Unused substitutes: Jones, Amos, Lokilo, Gomes, Robertson, Williams.
Burton: Garratt, Brayford, Carter, Bostwick, Hamer, Mancienne, Clare (Taylor, 45), Powell (Hemmings, 61), Edwards (Broom, 83), Akins, Fondop-Talom (Rowe, 61). Unused substitutes: O’Hara, Earl, O’Toole.
Referee: D Rock (Hertfordshire).
Revised kick-off times for Yorkshire clubs this weekend:
Premier League, Saturday: Wolves v Sheffield United, 8.15pm.
Championship, Saturday: Nottingham Forest v Huddersfield Town, 12.30pm; Sheffield Wednesday v Bristol City, 12.30pm.
Sunday: Rotherham United v Birmingham City, noon; Coventry City v Barnsley, 3pm.
League One, Saturday: Hull City v Fleetwood Town, 12.30pm; Shrewsbury Town v Doncaster Rovers 12.30pm
League Two, Saturday: Harrogate Town v Bradford City, 12.30.
National League, Saturday: FC Halifax Town v King’s Lynn Town, 12.30pm.
Women’s FA Cup, 4th round, Sunday: Huddersfield Town Ladies v Derby Ladies, 2pm; Middlesbrough Ladies v Sheffield United Women, 2pm.
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