Both sides had byes into the third round of the competition.
Thurrock made the progress to the last sixteen much easier of what the Millers did.
Thurrock travelled to Halstead Town, who beat Newham to get into the Third Round and Thurrock won on the night 5-1.
Aveley however, made it much more difficult progressing into the last sixteen as they travelled to Wivenhoe up the A12, and fought out a dire game of football as it finished 1-1, due to the Millers equalising one minute from time which was scored by AFC Hornchurch loanee Jamie Hursit.
The Millers then went on to win the penalty shoot out 7-6 on penalties. Marcus Elliott converted the penalty to make it 7-6, and then James Marrable saved the next one to send the Millers into the last 16.
Thurrock were given the toughest tie of the round as they hosted Conference Premier a League outfit Braintree Town, but on the night Thurrock were superb and defeated the Iron by four goals to one.
The Millers were also given a tough tie in the form of Conference South side Chelmsford City, whom came off a bad defeat away from home at Bishop Stortford.
The Millers battled and outplayed a fully strengthen Chelmsford side and in the end ran away 3-2 winners with goals from Mathias Bakare, Kyle Asante and the winner from Tyler Devlin.
Aveley FC v Thurrock FC (19th)
Billericay Town v Brightlingsea Regent (19th)
Dagenham & Redbridge v Concord Rangers (20th)
Redbridge v AFC Hornchurch (20th)