Eddie Johnson opened the scoring for Crewe forcing in Stephen Foster's pull-back at the far post following a corner that came from the visitors' first attack of the game.
Argyle, who had not scored for more than 500 minutes as they slumped to five consecutive defeats, bounced back to equalize within three minutes.
Matt Derbyshire, making his debut on loan from Blackburn, broke down the right and crossed for Scott Taylor to sweep home at the far post.
Try as both sides did for the remainder of the game, the two defences stood firm.
Argyle central defender Hasney Aljofree, who had earlier hit the crossbar with a header, saw Crewe goalkeeper Ross Turnbull, on loan from Middlesbrough, brilliantly block a fierce close-range effort.
At the other end, Turnbull's fellow keeper Romain Larrieu blocked a shot from Johnson that ended the Crewe striker's participation in the game as he pulled a hamstring in stretching for the ball.