After a slow opening it was the visitors who carved out the first opening after seven minutes. On-loan striker Izale McLeod found space just outside the Stockport box, but fired well wide.
At the other end Tommy Rowe pounced on a poor clearance from Lions' goalkeeper David Forde, but could only fire an effort from wide on the left touchline well wide of the gaping goal.
Millwall went in front after 17 minutes with an untidy goal from McLeod. Adam Bolder headed the ball forward and after Stockport keeper Owain fon Williams blocked an initial shot, McLeod bundled home a second attempt from close range.
In response, Gary Dicker headed a Rowe corner over for Stockport, but Jim Gannon's side were lacking something of a killer touch in the Millwall box.
Teenager Matty Mainwaring shot wide for Stockport, then left-back Michael Rose let fly from all of 30 yards, only for his shot to fizz just a foot over the crossbar.
Millwall doubled their lead eight minutes after the restart. David Martin played the ball through to the on-rushing McLeod and he was tripped by fon Williams as he tried to race round the keeper.
Mr Booth pointed to the spot, booked fon Williams and McLeod dusted himself down before coolly slotting home the penalty kick.
Tempers began to fray as Stockport tried desperately to get back into the game and after 64 minutes Millwall wideman Martin went off after picking up two quick yellow cards, but the hosts couldn't break down the visitors' stern defence.
Rose saw a cracking curling free-kick brilliantly saved by Forde, before sub McNeil got Stockport back in the game when he crashed home from close range on 79 minutes.
Just four minutes later it was back to 2-2 as Johnson's shot went in via a deflection off the unlucky Tony Craig.
McLeod almost nicked what would have been an undeserved winner for Millwall in stoppage time.