A first half penalty from Tom Maddison and a second half strike from Nat Watson did the damage, but in truth the margin of victory would have been greater but for some less than clinical finishing.
In the first half in particular Carlton repeatedly cut through the Daventry defence with some delightful approach play but they lacked the killer touch in front of goal.
Kieran Preston made an early save from Lewis Irwin but after that it was all Carlton. Tom Maddison, Aaron Opoku, Tyler Blake and Nat Watson all had chances to score but failed to test the goalkeeper. Opoku was at the heart of most of Carlton's attacks and he was fouled by Ross Harris for the penalty converted by Maddison.
Daventry always carried a threat on the counter attack and Carter Price missed their best chance, firing weakly at Preston from a good position.
Early in the second half Harris was inches from scoring an own goal when his attempted clearance from a Niall Davie cross hit the post but Carlton doubled their lead shortly afterwards when Watson fired home from the edge of the box after a lovely move.
The game became a much scrappier affair in the final half hour as Daventry pushed Carlton back and the Millers were grateful to some fine work from the entire defensive unit, with Dan Brown in particular outstanding as they picked up a third clean sheet in succession.
Carlton remain 6th in the table with 10 points from four games. They have a game in hand on the teams above them - Belper Town away - which has now been rearranged for Tuesday 21 September.
They return to action on Saturday when they entertain Stratford Town in the FA Cup.
A full report from today's match will be on site tonight.