An own goal from Peter Gilbert gifted the hosts the lead after David Healey had whipped in a vicious low cross.
And Northern Ireland international Healy's neat lob over Romain Larrieu a minute from time doubled their lead.
Plymouth substitute Stevie Crawford's last-ditch effort proved little consolation, despite the visitors showing plenty of promise early on.
Plymouth manager Bobby Williamson on Healy's goal:
"Sean Gregan had already been booked. Matt Doumbe played the ball back comfortably to the goalkeeper and then Gregan has come in and fouled him.
"So the ball gets played back by our goalkeeper, while Doumbe is still
rolling about and is on his way back up, but is playing Healy onside.
"It has been so costly because the referee and his assistant only assist when
they feel it's necessary."
Leeds: JSullivan, Kelly, Butler, Kilgallon,
Richardson (Carlisle 80), Lennon, Wright, Gregan, Pugh, Healy, Deane (Joachim 45).
Subs Not Used: Carson, Ricketts, Spring.
Booked: Gregan, Joachim.
Goals: Gilbert 46 og, Healy 90.
Plymouth: Larrieu, Connolly, Doumbe, Wotton, Gilbert, Norris, Hodges, Gudjonsson, Adams (Evans 66), Capaldi (Friio 52), Keith (Crawford 78).
Subs Not Used: Lasley, Aljofree.
Goals: Crawford 90.
Ref: G Salisbury (Lancashire).