It was the Dons who had the best early chance when wing-back James Furlong got in behind and picked out James Tilley, but his goal-bound effort was blocked on the line by the Daggers defence.
Referee Craig Hicks then went down with an injury and, following a lengthy stoppage, was replaced by fourth official Greg Rollason.
The stoppage dismantled the Dons' rhythm and the visitors were able to gain a foothold on proceedings, taking the lead when Morias' low 25-yard drive flicked off the inside of the post and into the net.
Furlong wasted a chance to equalise when he shot straight at Daggers keeper Elliot Justham.
But, five minutes later, Stevens bundled home the hosts' equaliser after the Daggers failed to deal with Furlong's left-wing cross, although replays suggested the striker was offside when the ball was played.
Josh Umerah's back heel went agonisingly across the face of goal at the start of the second half as the visitors began brightly, while Ryan Hill sliced an effort wide of the Dons goal.
The visitors limited the League Two side to shots outside the box and with 11 minutes to go, the game's deciding moment arrived.
After Dons keeper Owen Goodman failed to deal with Hill’s devilish inswinging corner, Rees was on hand to prod the ball past Josh Neufville on the line to send the travelling Daggers fans behind the goal into pandemonium and Ben Strevens' side into the next round.
Image source, Rex Features
