Argyle took a 25th minute lead through Reuben Reid's penalty following a foul on his strike partner Marvin Morgan by Rochdale goalkeeper Josh Lillis.
Dale responded with midfielder Matt Lund sending a dipping half volley just over the bar from 20 yards.
Lillis made a superb diving save to his left to keep out target man Morgan's downward header from skipper Conor Hourihane's 34th minute free kick. Hourihane did beat Lillis five minutes later but his curling right-footed shot hit the crossbar.
Argyle started on the front foot with Morgan heading just wide from Lewis Alessandra's cross from the right.
The Greens continued to force the pace and Reid should have done better at the far post when Lillis failed to hold Curtis Nelson's long, looping throw-in from the right.
Dale - managed by former Argyle central defender Keith Hill - pressed tirelessly for a leveller in the second half but rarely tested home keeper Luke McCormick.