Brown completed his treble in the 22nd minute - the earliest ever in a match by a Stags player - to secure only their third win of the season and stretch the unbeaten run to four matches.
Macclesfield, beaten on their travels for only the second time this season, have seen their last four matches produce 19 goals and they created plenty of half chances of their own despite the rout.
The Stags reshuffled the defence again with left-back injury victim Gareth Jelleyman returning as right-back for the suspended John Mullins - and within three minutes he had been booked.
But the yellow card failed to deter the home side who surged into a seventh minute lead.
Dan Martin's long free-kick was glanced backwards by former Stags defender Luke Dimech and, although keeper Tommy Lee rescued his side with a fine save to deny Matt Hamshaw from close range, Brown nodded in the rebound past the despairing dive of Lee.
The division's leading scorer Micky Boulding should have doubled the lead with his ninth goal of the season, but after latching onto Brown's clever lob, his close-range shot was blocked by the keeper.
But there was no let off a minute later in the 18th minute. Lee Bell's 35-yard free-kick was deflected onto the bar by Boulding, keeper Lee pushed the ball back up and Brown slammed the gift into the net from two yards.
The Silkmen had fallen apart defensively to Mansfield's incisive balls over the top of the defence and two further goals in two minutes - remarkably just two minutes later - hammered home the Stags' domination.
First Hamshaw's through ball allowed Nathan Arnold to run through and score from the edge of the area in the 20th minute and then from the kick-off Brown completed his hat-trick, racing clear again onto a Boulding flick-on and lobbing the keeper.
Macclesfield had their chances in an open first half and three minutes before half-time Francis Green was denied by the feet of keeper Carl Muggleton before ex-Stags' striker Martin Gritton wasted the rebound.
Then Martin slid across to block Green in injury time as the striker shaped to score.
Boulding's run and shot on the turn was well held by Lee as the Stags looked to add a fifth at the start of the second half.
But the division's leading scorer was not be denied and in the 54th minute he notched his ninth goal of the season, finishing clinically from one touch passes by Brown and Arnold.
Kevin McIntyre's low shot was held by the diving Muggleton as the Silkmen continued to create half chances of their own.
There was an amazing let-off for the home side ten minutes from time when Martin Gritton's shot was saved and substitute Gareth Evans fired the rebound against the bar and over from two yards.