Swans boss Roberto Martinez arrived looking to extend an unbeaten start to his managerial career to six games, but a sparkling performance from Harris combined with the 22nd-minute dismissal of Swansea skipper Alan Tate ensured a miserable afternoon for the visitors.
An eventful opening saw both teams suffer setbacks. When Millwall top-scorer Darren Byfield departed on a stretcher after a crunching challenge just seconds into the game, the home fans must have been fearing the worst.
But the odds quickly swung back in Millwall's favour, Swansea skipper Tate making two rash challenges within 12 minutes to earn an early bath.
Tate's dismissal left Swansea vulnerable at right-back, and with Leon Britton struggling to deputise effectively for his departed captain, it was no surprise when Millwall conjured the opener from that position.
Derby loanee Ryan Smith, making his full debut following a promising cameo against Port Vale, went past Britton as if the Swansea midfielder was a training cone, before delivering a wind-assisted cross that rebounded off the bar to Poul Hubertz. The big Dane squared the ball to Harris, who side-footed home to put the Lions ahead.
Harris nearly added another shortly afterwards after being put through by Tony Craig, but Swansea goalkeeper Willy Gueret was quickly out to smother.
But Harris did not have to wait too long to add to his tally. Boosted by the half-time introduction of talismanic striker Lee Trundle, Swansea had started the second half in determined fashion.
However, with 20 minutes to go defender Izzy Iriekpen brought down the irrepressible Harris just inside the area and the striker was quickly back on his feet to convert the penalty.
Millwall were unlucky not to add to their lead when Hubertz planted a glancing header too close to Gueret after another fine cross from Smith, but as the home crowd greeted every Millwall touch with cheers, nothing could ruin the Lions' afternoon.