Daryl Clare and John McGrath both scored twice to put 10-man Halifax to the sword in a 4-0 win and book Burton's place in the next round.
Two seasons ago the Brewers earned a money-spinning tie against Manchester United and boss Nigel Clough will again be dreaming of the third round after a clinical display at the Shay.
Halifax were facing an uphill struggle just 25 minutes in when referee Oliver Langford showed Anthony Griffith a straight red card for taking out Shaun Harrad through on goal.
Clare rubbed salt in the wound by curling the free-kick into the top right-hand corner despite goalkeeper Adam Legzdins getting a hand to it.
The visitors nearly doubled their lead two minutes later when debutant Michael Simpson struck the post from 15 yards.
Burton grabbed their decisive second goal just after the break following a defensive error by Cortez Belle.
The centre-back was caught dwelling on the ball and was dispossessed by McGrath, who buried the ball into the left-hand corner from 20 yards.
The game was effectively over after 63 minutes when Clare collected a neat flick from Harrad before slotting home, and Burton grabbed a fourth 10 minutes later as McGrath volleyed in from 10 yards.