Goals early in each half from Massiah McDonald and Ricky Gardner saw the Millers safely home in what was at times a frenetic game against a hard-working Eagles side.
The first half in particular was evenly fought and Arnold missed a golden opportunity to equalise in first half injury time after keeper Danny Marshall made a rare mistake.
But the Millers stopper redeemed himself in the second half with an excellent save from a Jason Lee header to record a fifth successive clean sheet.
Carlton join Hucknall Town and Eastwood Town in the last four, with the final quarter-final tie next Tuesday, 22 March, between Dunkirk and Wollaton. The draw for the semi-finals is expected to be made following this game.
A full match report will follow tomorrow. Photos are on site now.