Canaries academy product Chris Martin opened the scoring for the visitors after just four minutes of Saturday's League One clash with a low curling free-kick from 25 yards out - his 13th league goal of the season.
But parity was restored when full-back Craig's low shot from the left side of the penalty area found its way past the helpless Fraser Forster after 25 minutes, sending the home support into raptures.
Norwich right-back Russell Martin almost scored a wonder goal of his own just minutes before the interval, producing a mesmerising run from his own half into the Lions penalty area before firing wide.
Kenny Jackett's half-time reshuffle worked a treat, however, as substitute Harris headed home Chris Hackett's cross following a well-worked short corner to give the Lions the lead six minutes after the restart.
Millwall skipper Paul Robinson headed a good chance over before Hackett then went close with a 30-yard drive, while Forster lived up to his promising reputation with an instinctive one-handed save from Liam Trotter as Millwall threatened a third.