Leeds climbed out of the Championship bottom three thanks to Eddie Lewis' clinical finish at Home Park.
Robbie Blake gave them an early lead, latching on to Lewis' cut-back from the left to score his fifth in six matches.
With five minutes of the first half left, Bojan Djordic latched on to Tony Capaldi's free-kick to head home and he almost had a second shortly afterwards.
But Lewis decided matters when he beat the offside trap, latched onto Moore's pass and slid the ball past the keeper.
Plymouth manager Ian Holloway:
"We have to look at that Luton game on Tuesday and try to win it because I was expecting at least three points from this game.
"In fact I would have been disappointed if we'd only got one - and now, in the harsh reality of life, I got absolutely zip. It's a bitter pill to swallow.
"Our home form is not what we wish and we have to do something about it."
Leeds manager Dennis Wise:
"Eddie Lewis has done well, he took his goal well and set up the first one for us.
"The result has brought a couple of other teams closer to us whom we can now try to catch.
"Plymouth make it very difficult for you - so to be going from here with three points is pleasing. We got what we deserved."
Plymouth: McCormick, Connolly, Seip, Aljofree, Capaldi (Buzsaky 90), Norris, Wotton, Nalis (Summerfield 90), Djordjic (Chadwick 73), Ebanks-Blake, Hayles.
Subs Not Used: Larrieu, Sawyer.
Booked: Aljofree, Seip, Hayles, Ebanks-Blake.
Goals: Djordjic 40.
Leeds: Stack, Foxe, Heath, Kilgallon, Crainey, Douglas, Derry, Westlake, Lewis, Moore (Carole 80), Blake (Kandol 68).
Subs Not Used: Warner, Healy, Horsfield.
Booked: Westlake, Douglas.
Goals: Blake 3, Lewis 61.
Att: 17,088
Ref: D Whitestone (Northamptonshire).