Hull midfielder Regan Slater scored late in the first half to deny Plymouth victory at the MKM Stadium.
Adam Randell had given the visitors - who are yet to win on their travels this season - the lead, starting and finishing a neat move that flowed through Joe Edwards and Finn Azaz before finishing when Bali Mumba's cross was parried by goalkeeper Ryan Allsop.
Slater struck back for the home side, finishing off a low cross from Jaden Philogene, who had done brilliantly to keep the ball alive.
And Argyle were indebted to a fine goalkeeping display from Conor Hazard to protect the point in a frantic second half.