Both sides made several changes to their starting line-ups but Millers eventually ran out worthy winners.
Maidstone started strongly and took the lead through Lloyd Blackman. The Stones forward beat the off-side trap and chased a long ball before lobbing over the advancing Marc Palmer.
The visitors continued to hold the upper-hand but the Millers defence held firm.
Aveley were given a way back into the game when Sean Thomas was brought down when chasing a loose ball on the six yard line. Wayne Vaughan stepped up and put away the spot kick with the Stones keeper choosing the wrong side.
Thomas then had a chance to give Millers the lead. An excellent cross from Sam Holloway was met with a firm header but the ball went wide of the far post.
Christian Wheeler put Aveley into the lead shortly after half time. A shot following a corner took a slight deflection off a Stones defender and nestled in the corner of the net.
Joao Carlos sealed the win with a screamer of a shot from the edge of the penalty area. Collecting the ball about 35 yards out he held off a chasing defender before unleashing an unstoppable shot into the top left-hand corner.
Millers now enter the draw for the third round which will be made this Friday, 5th December. The next round of matches are due to be played week commencing Monday 6th January.