Bryson's hat-trick was bookended by goals from Jake Buxton and Mason Bennett, as the Rams destroyed the Lions in every area of the pitch.
Buxton put Derby ahead inside the first 10 minutes.
Jamie Ward's corner was cleared back to him by goalkeeper David Forde, but he crossed again to the back post where Buxton defeated Danny Shittu's lax marking to head past Martyn Woolford.
The early goal established a superiority Derby were never to relinquish and rammed further down Millwall throats as the game progressed.
The dominance stemmed from the relentless energy of the two more advanced midfielders in Derby's 4-3-3 formation, Bryson and Will Hughes.
Hughes' continuing appearance in the Rams ranks will be of considerable relief to Derby supporters amid eight-figure attention on transfer deadline day and showed exactly why he has attracted such speculation.
Despite technical ability and movement, he was even more impressive without the ball. He pressed Millwall's defence and midfield into mistakes all afternoon, particularly the embattled Shane Lowry, who was repeatedly forced to waste possession with long balls and responded by with a late, second-half tackle on Hughes that saw him sent-off.
But ultimately Bryson stole Hughes' thunder. His first two goals were stunning finishes.
Just as Derby's first-half ascendancy was threatening to go relatively unrewarded, Shaun Derry cleared Ward's free-kick into Bryson's path. The Scottish international took one touch, before unleashing a fierce shot home from 20 yards.
Shortly after half-time improbably he scored an even better goal. He slammed home a powerful drive once more, this time from slightly further out as Derby broke quickly from the back.
After Martyn Waghorn grabbed an irrelevant consolation on his Millwall debut, Bryson sealed Derby's first hat-trick since 1996, completing another slick passing move.
Hughes broke forward, passed right to Kieron Freeman, who played in Bryson to poke home. Every step of the process was far too easy for Derby, as Millwall squandered any comeback they may have threatened.
Derby's day got even sweeter late on as 17-year-old substitute Bennett rounded off the result with another fine finish.
For the Lions, the gradual improvements they had been showing under Lomas with two away draws following three defeats were unequivocally blown out of the water.
The midfield were outnumbered with Derby always having an extra man to pass to, even before the sending-off. The defence's distribution was abysmal and they were slow to respond to the fluid movement of Derby's front five.
The forwards were the most blameless as they were restricted to chasing long punts from the back and Scott McDonald and Waghorn combined nicely for the latter's goal.
Lomas tried to respond by pulling Andy Keogh in midfield to remove Derby's extra man. This worked to an extent, but as his midfield slowly regained something near a foothold, he pushed Keogh back into the forward line and conceded a second goal shortly after.