Over 1,500 fans saw plenty of effort but the Championship club eased through 3-0 as the final National League club standing couldn’t pull off a big shock.
Mihailo Ivanovic’s moment of unorthodox brilliance opened the scoring.
Caspar De Norre arrived at the back post hands the Daggers an almighty task before Ra'ees Bangura-Williams minutes into his professional debut made it safe.
Dagenham’s caretaker manager Lewis Young said: "I was disappointed a little bit at half-time, I didn't think the players showed themselves.
“You know when you're on a big stage and you've got a chance to go and show everyone, there was a little bit of fear, a bit of enormity and the size of the stadium and players they're facing.
"There was a 20-minute period in the second half where we had a couple of chances and had them really on the back foot.
"Ultimately they're a Championship club but I'm so proud of that 20-minute period and the reaction."
At the full time whistle, the Daggers’ players and staff saluted their supporters who kept singing all night.
It is the Lions who will go on to face Leeds United in the next round after their professional performance.
PHOTO BY JIMMY McDONALD