Romaine Graham and debutant Joe Fitzpatrick did the damage with a second half brace apiece after Daniel Gordon had opened the scoring in the first half.
Tividale were level before half time thanks to a Chris Sterling penalty and Sterling gave the visitors the lead early in the second period with a curling effort.
With the possibility of dropping into the relegation zone staring Wayne Scott's team in the face, they raised their game, laid siege to the Tividale goal and got their reward with four goals in the final quarter of the game.
The win leaves Carlton 20th in the table but with a three point gap to Loughborough just below them and within reach of a host of teams just above them.
A match report will be on site shortly.
The Millers return to action on Wednesday evening at home to Barwell in the league cup.