Injury-hit Argyle were undone by Andy Drury's measured 22nd minute strike through a crowded penalty area as the greens failed to clear their lines following a corner.
The Pilgrims had plenty of first half opportunities to have won the game with new loan signing Olly Lee and skipper Curtis Nelson forcing good saves from Hatters keeper Mark Tyler.
Reuben Reid, another who went close in the first half, created Argyle's best second half chance, firing the ball across the face of goal from the left. It was the sort of cross that top scorer Reid has frequently converted.
Argyle boss John Sheridan said: “I didn’t think there was anything between the two teams apart from the goal, which just changed the game.
“They kept a tight shape after that, which they are good at. I don’t think it was a lack of effort but we just seemed to be a bit short of sharpness that we usually show at home.
“I don’t think we have caused them enough problems, especially in the second half. We have huffed and puffed. One or two balls went into the box from wide areas but we just didn’t get the rub of the green or work their keeper too much.
“I thought we played okay in the first half and I don’t want to use the excuse of the injured players but then Lee Cox had to come off at half time, Dominic Blizzard during the second half and then when Tyler Harvey went on he got injured straight away..."
SWSN star Olly Lee
Argyle injury list
River Allen groin
Jason Banton hamstring
Dominic Blizzard hamstring
Lee Cox thigh
Peter Hartley hip flexor
Tyler Harvey unspecified
Andy Kellett groin
Marvin Morgan unspecified
Ollie Norburn back
