Joel Daft gave the Millers the lead on five minutes when he was on hand to snap up a loose ball after Kai Moore had seen his effort blocked.
But ex-Miller Jake Carlisle drew Heanor level on 14 minutes, heading home unmarked from a corner.
Heanor pushed forward and were rewarded just before the half hour when Lewis Weaver ran onto a through ball, rounded goalkeeper Tomasz Bukowski and slotted home.
Heanor’s lead lasted just three minutes. Holmes and Dan Flynn combined to play the ball to trialist who rifled home from the edge of the box.
Trialist got his second on 37 minutes to restore Carlton’s advantage when he showed neat footwork to steer the ball into the net following a Daft free kick.
Tommy Brookbanks, who had started the game with only two first team regulars from the last couple of seasons, brought more development players on in the second half but the game remained closely contested.
Heanor deservedly levelled on 72 minutes when Jack Desmond found himself unmarked from a free kick and headed past Bukowski.
Four minutes later trialist bagged his hattrick, running onto a lovely pass from Daft and slotting home at the near post. But Heanor were not finished and with 10 minutes remaining Kyle Daley lashed the ball into the corner of net from 25 yards after Carlton had given up possession cheaply.
The home side almost won it in the last few minutes when a cross from Harry Joves flew over everyone and struck the far post before being cleared. Both sides will be pleased with their attacking play and both sides will feel they have a little work to do on their defending as pre-season continues.
Carlton Town: Bukowski, Cockram, Quinn, Brown, Johal (Rio Joseph), Holmes (Sonny Shaw 63), Flint (Ellis Tongue 59), Matthews, K Moore (Isaac Hayes 65), trialist, Daft.
Goals: Daft 5, trialist 32, 37, 76; Jake Carlisle 14, Lewis Weaver 29, Jack Desmond 72, Kyle Daley 80