The closest Kevin Blackwell's side came to scoring came nine minutes before the interval when the recalled David Healy cracked a shot against the post.
Indeed, the visitors could have won had any player converted Leon Clarke's volley across goal in the second half.
Plymouth manager Tony Pulis on Leeds midfielder Liam Miller tangled with David Norris:
"I thought it was a stonewall penalty at the end when Miller fouled Norris.
"It was two yards inside the box and that's happened to us three times in three weeks now. It happened against Wolves and Preston as well.
"It was scrappy in the first half but we stepped it up after the break and created some good opportunities. Neil Sullivan made the save of the game from Leon Clarke. But obviously I'm biased - I see everything through green eyes."
Leeds: Sullivan, Kelly (Beckford 36), Butler, Gregan, Crainey, Richardson, Derry, Douglas (Miller 74), Healy (Lewis 68), Hulse, Blake.
Subs Not Used: Bennett, Kilgallon.
Plymouth: Larrieu, Connolly, Doumbe, Aljofree, Hodges (Pulis 90), Norris, Wotton, Nalis, Capaldi, Pericard (Buzsaky 87), Clarke (Evans 71).
Subs Not Used: McCormick, Zebroski.
Booked: Nalis, Connolly, Larrieu.
Ref: M Thorpe (Suffolk).