Goals in each half from Rossi Jarvis and substitute Tristan Plummer gave the Hatters - bottom of the Football League - a deserved win against a disappointing Pilgrims outfit.
The visitors, who were poor in the first half, only livened up after the introduction of Rory Fallon at half-time and did have the ball in the net in the 62nd minute only for Steve MacLean's effort to be chalked off for a foul.
Luton bossed proceedings from the off, just as they did against Port Vale at the weekend.
Graham Stack had to produce a superb double save in the sixth minute to firstly keep out Chris Martin's 10-yard header from Kevin Nicholls' left-wing cross, before somehow denying Jarvis' follow up on the goalline.
Jarvis made no mistake in the 15th minute as he gave the hosts a richly-deserved lead by blasting home on the half-volley with his right foot from 12 yards out after Martin's precise pull-back from the right byline.
Plymouth eventually began to produce football that hinted at their higher league status, but all they had to show for their possession was a mis-hit far post effort from midfielder Simon Walton, which flew harmlessly wide after Jason Puncheon's cross from the right.
MacLean finally broke free from the shackles of the excellent Michael Spillane in the 42nd minute but, after his clever turn on the edge of the area, he could only shoot weakly at Brill left-footed.
Instead, Luton almost stretched their lead seconds later when a scramble on the edge of the six-yard box saw Krisztian Timar deny Sam Parkin with a timely challenge.
Argyle brought on Luke Summerfield and Fallon for the ineffective Yoann Folly and Jermaine Easter and showed immediate improvement.
Firstly Fallon headed Puncheon's cross over from 10 yards in the 50th minute and two minutes later Puncheon sent a low left-foot drive just wide from the right-hand corner of the penalty area.
Plymouth thought they had equalised in the 62nd minute when Fallon headed on Puncheon's corner for MacLean to convert on the line, but the effort was disallowed for an infringement in the area.
Luton sealed the win 13 minutes from time when a Plymouth clearance rebounded off substitute Jamie Mackie into the path of Asa Hall, who hit a shot which Stack could only parry, allowing Plummer to convert on the goalline.