Ashley Chambers had already brought a terrific near-post stop out of Argyle stopper Jake Cole when he broke the deadlock in the 20th minute.
The winger started the move and then darted into the box where he got the ball back from Adam Reed via Cresswell's shin before dinking the opener over Cole.
The Pilgrims found themselves further behind nine minutes later courtesy of Cresswell, who was playing at Bootham Crescent for the first time since coming back to his former club on loan from Sheffield United.
From the hosts' corner, Luke Young managed to clear Tom Platt's header off the line but 35-year-old Cresswell was on hand to instinctively nod home.
Plymouth boss John Sheridan made three substitutions quickly after the break and Maxime Blanchard came close when he flashed a header past the far post.
However, the Minstermen were virtually untroubled as they recorded their first win since New Year's Day.