Straight from the kick-off, a cross from the left by Clive Clarke resulted in a chance for Kenwyne Jones but his shot deflected wide off Hasney Aljofree.
In a fast start, Argyle piled forward in the second minute but, as was the story at the other end, Dexter Blackstock shot wide of Steve Simonsen's left-hand post.
The visitors went even closer six minutes later when out of nothing, Akos Buzsaky hit a blistering 20-yard shot that crashed off the crossbar.
However, it was Stoke who took lead on 28 minutes when a chip across by David Brammer was attacked by the arriving Jones who sent the ball into the net.
The Potters should have doubled their lead two minutes later, but after beating Graham Coughlan, Gifton Noel-Williams skied a 12-yard shot.
Plymouth continued to plug away but Simonsen repelled Micky Evans' close-range shot after 36 minutes.
City did score again before the break when a lay-off by Noel-Williams gave Darel Russell the opportunity to shoot. The midfielder's 30-yard drive took a deflection off a static Buzsaky to send Luke McCormick the wrong way and the ball into the back of the net.
Chris Greenacre's efforts were almost rewarded in the 65th minute when he tried to guide home a Jones cross, but a fantastic save by McCormick prevented his side going further behind.
David Worrell's 90th minute volley was the closest that Plymouth came to a consolation goal but another save by Simonsen denied even that.