On-loan Tottenham man Harry Kane scored the others as the Championship side proved their dominance over their League Two counterparts.
The home side took the lead with their first attack of the game as Henderson pounced on Kane's mis-hit shot to lash home.
Henderson returned the favour to Kane by laying in the midfielder, whose shot from the edge of the area eluded Daggers keeper Chris Lewington.
Henderson completed his hattrick after the break by tapping into an empty net after 59 minutes before converting a penalty four minutes later.
Kane notched his second of the night soon after to complete the rout and send Kenny Jackett's men through.
The Lions welcome Championship leaders Southampton to the New Den in round four.