The Iron fought back from 2-1 behind to emerge victorious, with former York City winger Martyn Woolford grabbing the winner five minutes from time.
Scunny were boosted by the return of leading scorer Gary Hooper after injury and they made a perfect start by taking the lead after just six minutes.
A couple of excellent flicks released Woolford, his shot was parried by David Forde, but Matt Sparrow was on hand to blast home from close range.
Woolford fired narrowly over the top as Scunny pushed for a second goal and Hooper struck a post, before the Lions responded with Zak Whitbread shooting on target and Lewis Grabban having an effort blocked.
Just before the half-hour mark Grant McCann's mis-hit shot reached Woolford at the far post and Forde made a brave save at the feet of the Iron winger.
Soon after Neil Harris did superbly to find Dave Martin and his shot was deflected by Sam Togwell on to an upright and away from goal.
However, eight minutes before the interval MIllwall were level thanks to an incredible strike from Gary Alexander.
He chested the ball down over 35 yards from goal on the left and arrowed a superb right-foot strike over the stranded Murphy.
Two minutes later it was 2-1 to Millwall as Alexander headed goalwards from a Martin cross from the left and Murphy fumbled the ball over the line.
The early part of the second half was far less frantic than the first had been, with both sides struggling to forge any clear chances.
However, just past the hour mark it was nearly 2-2, as Forde blocked Liam Trotter's shot from a corner and then three Lions defenders got in crucial headers to clear the danger.
Twenty minutes from time Scunny found an equaliser, as Woolford did superbly down the left and his ball across the face of goal found Sparrow, who turned inside Forde and buried his shot.
Six minutes later Alexander suffered a nightmare moment, as he headed wide from six yards out following a Chris Hackett cross from the right.
That miss proved decisive when Woolford struck near the death, with a long free-kick into the area eventually falling to the wideman who rifled a left-footer under Forde from ten yards out.