Enzo Maresca enjoyed a dream FA Cup bow as a manager to put him back on the road to Wembley.
The Leicester boss was part of Pep Guardiola's coaching staff when Manchester City won the trophy last season.
But this was the first time he had taken charge of a team in the competition and goals from Cesare Casadei, Ricardo Pereira and Tom Cannon made his day.
Millwall, who scored goals of their own through Duncan Watmore and Zian Flemming, were often the better side here but missed a host of chances.