The Lions striker netted from close range with just six minutes remaining, although the Coventry defenders were adamant that Harris was in an offside position when he received the vital pass.
Until then, the Sky Blues looked as if they would leave The Den with a creditable draw after veteran full-back Steve Staunton had cancelled out Paul Ifill's goal.
Staunton stepped up to the penalty spot on 70 minutes after he himself had been tripped in the box by Matt Lawrence and fired low and hard into the bottom corner to give keeper Tony Warner no chance.
The goal put Coventry level after Ifill's close-range effort had given Millwall the lead just eight minutes earlier.
Tony Craig's long throw caused chaos in the box and although the visiting defence managed to block Ifill's first effort, he turned and hooked the ball in from a tight angle.
Millwall played the last few seconds with only ten men as Tim Cahill was sent off for two bookable offences, but they held on for a win that keeps them on the fringes of the play-off zone.