The result means that Carlton will be in the Third Round Qualifying draw for the first time in their history on Monday as the sides will meet again on Wednesday night at Stoke Lane in the replay.
Steggles produced a number of excellent saves to deny the hosts, who controlled the majority of the game. In particular, a late second half save from a Jimmy Spence header was outstanding, springing to his left to tip away a goal-bound bullet point effort.
Carlton did create the occasional opportunity and had a glorious opportunity to steal victory in added time when Connor Bartle and Joe Brothwell broke clear but home goalkeeper Kyle Trenerry read the situation well to clear Bartle's pass.
Both sides had the ball in the net only to be thwarted by offside flags, and the Millers defence and midfield worked tirelessly to keep their Premier Division opponents at bay, with Riece Bertram and Henry Rollinson particularly impressive.
Ultimately it was Steggles whose saves earned the replay in which Carlton will hope to cause another cup upset after beating step 3 Bedworth in the last round.
A full report from today's game will be on site tomorrow.