Goals from Andre Gray and Alex Lawless helped Luton end Blue Square Bet South side Dorchester's FA Cup run.
The Hatters began the stronger and were rewarded when Gray raced through to fire home from 10 yards.
Lawless then doubled the hosts' lead when he drove into the bottom corner.
Arran Pugh's header gave the first round conquerors of League Two side Plymouth hope, but Ben Watson, Sam Malsom and Jake Gosling could not find a way past Luton keeper Mark Tyler.
VIEW FROM THE DRESSING ROOM
Dorchester Town FC boss Phil Simkin tells BBC Radio Solent:
"I can't speak highly enough of the players, they were absolutely magnificent.
(On Dan Thompson) "Dan did really well, he's a big, big lad and raw at the moment but he wants to learn. He did well when he came on.
"The FA Cup's been great for all of us. It's given us a lot of confidence, it's brought in a lot of financial assets as well."