The veteran frontman, who was only playing because on-loan Leeds striker Tresor Kandol was ineligible, headed home just before the hour and sealed the win two minutes from time with a smart finish.
Leeds went ahead with their first attempt on goal on the half hour when Neil Kilkenny slipped the ball into Argentine striker Luciano Becchio, who swivelled and fired a stunning 20-yard shot beyond David Forde for his fourth goal of the season.
But the Lions were level seven minutes later when the lively Dave Martin lifted the ball over David Lucas after good work from the hard-working Harris.
The Lions started brightly after the break and went ahead on 59 minutes when Harris headed Marc Laird's cross past Lucas.
Millwall's all-time leading scorer made the game safe in the dying minutes when he curled a shot into an unguarded net after Lucas made a mess of a routine through ball.