Three first half goals set Town on course for a 4-0 win at Moulton in Saturday’s first round tie.
Daventry’s goals came from Sam Heavey, Ryan Chamberlain, Aaron King and substitute Elliott Lamb-Johnson. Daventry now visit Wellingborough Whitworths in the next round.
Moulton started the game well and came close when Luke Archer headed Ash Brown’s corner onto the bar. Town began to get a foot hold in the game and Adam Creaney hit the post from a swerving shot from outside the area.
Creaney also brought a good save from Wayne McDonald, the keeper getting down well to turn his shot round the post.
Town broke the deadlock in the 31st minute when Jordan Orosz was brought down in the area by Aaron Blundell and Heavey stepped up to convert the ensuing spot-kick past McDonald.
Town doubled their advantage in the 36th minute when Creaney’s corner fell to King who beat his marker and crossed to the far post, where Chamberlain headed home.
James Tricks headed Creaney’s cross just wide before King made it 3-0 on the stroke of halftime with a neat finish over McDonald from ten yards.
Town started the second half as they ended the first, with King, Ross Harris and Lamb-Johnson all having chances.
Substitute Scott Cross also had two chances, first after Lamb-Johnson ran from his own half and played the ball through, only for McDonald to save with his legs. Cross also dispossessed a Moulton defender and lobbed the keeper from 20 yards only to see the shot go just over.
Cross turned provider in the 85th minute, his searching pass found Lamb-Johnson and the winger finished well past McDonald.
Moulton were harshly reduced to ten men when right-back Sam Ruggan was shown a straight red after a slightly late challenge on Heavey.