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Deep into first-half stoppage time, Mills picked the ball up 30 yards out and drove a piledriver past Tony Warner to hand Coventry the lead.
The goal was a fitting end to a brilliant first half which saw City take the lead after 30 minutes.
A Gary McAllister corner found Stuart Nethercott who mishit his clearance straight towards his own goal. Ronnie Bull blocked bravely, but nippy Gary McSheffrey popped up to tap in from point-blank range.
The lead was short-lived, though, as Millwall hit back eight minutes later through on-loan Southampton striker Kevin Davies.
Fabien Debec should have claimed the ball when it came back off his left-hand post from Christophe Kinet, but his hesitancy allowed Davies to stab home.
But Mills had the last word of the half with his electrifying shot deep into stoppage time.
Millwall came out quickly from the break and had equalised within five minutes.
Nethercott's free-kick found the head of Davies, who set up Kinet for a fine volley on the turn to silence the home fans.
Paul Ifill could have sealed all three points for the visitors as he beat the offside trap and left the defence standing, but Debec saved well with his legs.
But a goal was coming and Harris was given far too much time to control with his back to goal in the 85th minute.
With three defenders around him, but none challenging, he turned and beat Debec from eight yards to make sure the Lions took all three points.