After a good start they fell behind early in the second half when Clark Carlisle inexplicably handled the ball in his own area.
Dean Ashton fired home the penalty but almost immediately Leeds equalised when Pugh followed up Paul Butler's effort on goal to score.
A drilled Steve Jones shot restored Crewe's advantage but with the whistle beckoning Pugh thundered in a second.
Leeds boss Kevin Blackwell:
"Their goals came out of nothing but we showed great character to fight back not once, but twice.
"We were good enough and should have won the game but we didn't finish it off.
"We were doing so well, the strikers were missing but thinking another chance would come along. You have to finish these games off and we didn't do that - it's a lesson learned."
Crewe: Williams, Moses, Walker, Foster, Tonkin, Sorvel, Lunt,
Vaughan, Ashton (Higdon 86), Steve Jones, Varney (Cochrane 45).
Subs Not Used: Ince, Mark Roberts, Rivers.
Goals: Ashton 48 pen, Steve Jones 83.
Leeds: Sullivan, Kelly, Carlisle, Butler, Crainey, Wright,
Gregan, Richardson (McMaster 85), Pugh, Joachim (Ricketts 69),
Subs Not Used: Carson, Spring, Duberry.
Goals: Pugh 53, 89.
Ref: P Joslin (Nottinghamshire).