Full-time from The Den
O'Brien marked his first start in nine games with a super 12th-minute strike to put The Lions on the way, and top scorer Gregory capped a fine display with his 23rd goal of the campaign just six minutes later.
It proved the perfect response to the disappointment of Saturday's narrow defeat at Bradford City, but was a result that also saw The Lions climb back up to fifth in the table having temporarily slipped down to sixth place with Play-Off rivals Wigan, Gillingham, Bradford and Barnsley all winning earlier in the day.
Table-topping Burton were unchanged from the team that were surprisingly held to a goalless draw by struggling Oldham Athletic at the weekend, although loan signing Tyler Walker did join up with the squad having been on international duty with England U20s against Canada.
The Lions started brightly and showed their attacking intent within two minutes when a strong run by Steve Morison enabled the skipper to work an opening and send over a low cross that Taylor met first-time, but was only able to flick straight into keeper Jon McLaughlin's hands.
Byron Webster was perfectly placed to make a timely interception at the other end from Mark Duffy's floated free-kick and then Lions keeper Jordan Archer reacted smartly to push Duffy's low drive away.
However it was Millwall who opened the scoring on 12 minutes with a goal that owed as much to a fine finish from O'Brien as it did to the build-up play. Diminutive midfielder Ben Thompson expertly hooked the ball forward from deep in his own half, Gregory picked up the pass and used his strength and skill to hold off three players before laying off a perfectly weighted pass to O'Brien, who smashed an unstoppable shot into the top corner from 16 yards.
Just six minutes later The Lions had doubled their tally; this time Williams threaded a sublime through pass to Gregory who took one touch to guide the ball beyond onrushing keeper McLaughlin, and then kept his composure and steered home into an empty net.
An acrobatic tip-over from Archer kept out the dangerous Duffy's deep 21st-minute free-kick, but it was Millwall who looked the more likely of the two teams to score - and were a whisker away from doing just that when another intelligent pass from Williams fed O'Brien, his dinked cross was met by the head of Gregory but the top-scorer contrived to steer his header over the bar from a central position.
Burton boss Clough introduced Walker at the start of the second-half in a bid to fire a response from his team, but Harris' charges produced another confident, composed 45 minutes in which they confidently dealt with anything Burton threw out them, and created chances of their own to add further goals.
An inviting delivery by Morison was claimed by keeper McLaughlin under pressure and then the skipper' headed Williams' free-kick back across goal with O'Brien inches away from connecting.
Mark Beevers, outstanding in the heart of defence, made a timely interception to avert the danger with Hamza Choudhury ready to pounce as Burton tried to get a foothold back into the game, but were simply blocked at every turn.
It was The Lions who could have added further goals, as they attacked with real zest and creativity.
Thompson was unlucky when his drilled angled pass flashed just beyond the reach of Gregory, whilst the latter saw a 79th-minute penalty appeal turned down after he went to ground under a challenge from Tom Flanagan as he prepared to pull the trigger.
Gregory then won possession from Phil Edwards and slid the ball into Thompson's path, but the youngster's shot at full stretch was blocked by McLaughlin to deny him a goal his performance deserved.
Sub Jamie Philpot was a whisker away from connecting with Thompson's through ball, only to be denied as McLaughlin sprinted out of his goal to avert the danger as the game entered the injury-time.
There was to be no way back for Burton, however, with Millwall expertly working down the five minutes of injury-time to secure three precious points and an impressive fifth successive clean sheet at The Den.
Booking: Thompson (21mins), Beevers (73mins), J.Martin (88mins), Romeo (90+2mins)
Scorers: O'Brien (12mins), Gregory (18mins),
Burton Albion: McLaughlin, Edwards, Mousinho, Beavon (Bennett, 63mins), Akins, Butcher, McCrory, Naylor (Walker, 46mins), Duffy (Harness, 86min), Flanagan, Choudhury. Subs not used: Bywater, Cansdell-Sherriff, Reilly, Weir.
Bookings: Mousinho (22mins), Beavon (42mins), Butcher (73mins)
Att: 8,012 (away 244)
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