The Glassboys took the lead in the 18th minute when Brian Smikle was on hand to finish a low cross from George Bowerman, and Bowerman himself doubled the advantage on 23 minutes with a clever lob after being set up by Drew Canavan.
But Carlton were quick to dispel any ideas of an easy passage, as Alex Troke slotted home after Dean Coleman had been unable to hold Josh Rae's header.
The Glassboys restored their two-goal advantage eight minutes after the break when from another Bowerman cross from the left, Smikle hit a low shot that went in off Will Richards and Canavan snuffed out any lingering hopes the Millers may have had on 82 minutes as a shot from distance by Canavan beat Curtis McDonald.
The visitors were determined to go down fighting, however, and it was Aaron Hooton who completed the scoring four minutes from time.