The Railwaymen led twice in the second half against Kevin Blackwell's team. But their advantage was short lived and Pugh cancelled out a Dean Ashton penalty and a late finish from Steve Jones with a thumping drive a minute from time.
Crewe started the stronger and carved out decent openings in the first 45 minutes as Leeds looked hesitant on their first ever visit to Gresty Road.
Jones hit a rising drive over Neil Sullivan's cross bar in the 21st minute and came even closer three minutes later when he flicked on a Kenny Lunt free-kick with his head, only to see Sullivan palm the ball over the bar.
Leeds responded and the hosts were lucky to escape with their goal intact in a flurry of chances around the half-hour mark.
Former Manchester United youngster Pugh, who was always looking to drive Leeds forward, forced home keeper Ben Williams to tip a fierce drive around the post and then headed wide from a Jermaine Wright cross.
Midfielder Wright then thumped the base of the post and Frazer Richardson's effort from the rebound was headed off the line by Steve Foster, as Leeds came close to grabbing the opener.
But some slack defending from Clarke Carlisle gifted Crewe the lead after 47 minutes. The centre half's trailing arm met Richard Walker's header and Ashton made no mistake with a low shot beyond Sullivan with the resulting penalty.
The Railwaymen were in front for only five minutes. Leeds debutant Sean Gregan lifted the ball into the box and Julian Joachim headed onto the bar. And before any Crewe defender could react, Pugh followed in to ram home a close-range header for the equaliser.
Wright and Brian Deane came close with a shot and a flashing header as Leeds began to dominate.
Crewe were still dangerous on the break, in particular the speedy Jones, and he had a goal ruled out for offside ten minutes from time when he cut in from the left hand side of the box and shot past Sullivan.
The Northern Ireland international wasn't to be denied and he handed Crewe the lead again in the 82nd minute.
David Vaughan found Lunt inside the box and the Crewe captain shielded the ball intelligently before laying it off to Jones, who found the bottom corner with an angled drive to send the home faithful delirious.
However, their joy was short lived as Leeds raised the pressure and, in the 89th minute, Pugh met Wright's driven cross with a thunderous half-volley which flew past Williams.