Liam Feeney scored the only goal of the game, drilling the ball into the net after a low right-wing cross from Smith. Millwall will host Aston Villa in the fourth round.
In League Two, Jordan Archer played in goal as Wycombe beat Chesterfield 2-1 to move up to 11th in the table.
Harry Kane and Nathan Byrne were both unused substitutes in their games for Norwich and Crawley Town respectively.
John Bostock has returned to the Club following the end of his loan spell with Swindon Town.