The midfielder, who was one of the seven academy players to gain first team experience for the club in their Checkatrade Trophy group stage campaign recently, opened the scoring on just nine minutes when he curled a wonderful effort into the net from 20 yards.
Freddie Hinds had the opportunity to double the host’s lead shortly afterwards from Kavan Cotter’s through ball, only to see Scott Mitchell produce an excellent challenge.
Daggers had their moments too though, with Tyrique Hyde’s effort cleared off the line by Jack James, while Tiernan Parker did well to deny Joe White.
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The visitors were level on 40 minutes though when Dylan Florence found the bottom corner, while he notched his second seconds before the break to put Daggers 2-1 up.
In the second period, Tyreeq Bakinson was narrowly side from range, as was Hyde, before Arthur Read saw his curler stopped by keeper Joe Carter at his near post.
Read, who made his first team debut against Millwall recently, was on target though with nine minutes to go, hammering into the bottom corner.
In the first period of extra time, Florence completed his hat-trick as Daggers led once more, before Snelus took over, scoring on 111 minutes from the edge of the box, and then winning the tie with a scorching drive into the top corner just two minutes later.
Hatters will now travel to Sheffield Wednesday in the next round.
Hatters: Parker, Bean, James, Bakinson, Mead, Jones (Sorunke), Cotter ©, Murray (Shamalo), Hinds (Tomlinson), Read.
Daggers: Carter, Walker-Brown (Agboola), Gordon, Brown, Lee, Mitchell, Bonds, Hyde (Turvey), White, Florence, Mongoy.