Rotherham burst into an early lead when a Dale Tonge cross from the right was met by a towering header from Nick Fenton after seven minutes.
The home side came close to stretching their lead when Reuben Reid pounced onto a loose ball on the right but Harrison did well to block him.
But Barnet were level 11 minutes later when Albert Adomah's inch-perfect cross from the right found Luke Medley unmarked and he headed past Andy Warrington.
Rotherham should have reclaimed the lead after 30 minutes when Micky Cummins picked out Alex Rhodes, who raced through but was cut down in the area by Max Porter earning the Barnet defender a red card.
But Mark Hudson's tame penalty was saved by Harrison and nine minutes before the break the visitors went ahead when Adomah produced a stunning goal with a fierce angled shot as he cut in from the right.
Barnet sealed the win when Cliff Akurang grabbed two goals early in the second half to stun the home side.
The first came in the 57th minute when he went on a weaving run as Rotherham's defence stood off before slotting a cool shot past the helpless Warrington.
And when the home defence was caught out again, Akurang latched onto the ball and danced his way through several challenges before rounding Warrington with ease for the fourth.
In the 69th minute Rotherham pulled one back when Ian Sharps headed in a free-kick crossed in by Tonge and Mark Burchill scored a penalty ten minutes from the end as the home side rallied.
Nick Fenton hit the woodwork in stoppage time, as the Millers wasted enough chances to have won two games but came away empty handed leaving Bees stopper Harrison the hero.