Marcel Seip headed into his own net to give Stoke the lead but went from hero to villain when he nodded home to draw Plymouth level.
Peter Halmosi's header fell to Rory Fallon to stroke the ball home and put the visitors ahead before Liam Lawrence scored for Stoke from six yards.
The home side secured the win when Fuller lobbed a Stephen Wright cross past Plymouth keeper Luke McCormick.
Stoke manager Tony Pulis:
"Some of the crowd started to have a moan and groan at 2-1 down and I felt like moaning and groaning myself. We were very flat at the start of the second half.
"But perhaps the crowd having a go helped us because the players picked it up after that."
Plymouth manager Ian Holloway:
"We let two goals in from free-kicks when we had every single player back defending. There is no way that should happen.
"The players didn't organise themselves correctly and we didn't have enough leaders out there to sort things out."
Stoke: Simonsen, Zakuani, Shawcross, Hill (Wilkinson 47), Wright, Lawrence, Delap, Matteo, Cresswell (Sweeney 64), Sidibe (Parkin 88), Fuller.
Subs Not Used: Hoult, Eustace.
Goals: Seip 10 og, Lawrence 66, Fuller 73.
Plymouth: McCormick, Connolly, Timar, Seip, Sawyer (Hodges 89), Norris, Nalis, Buzsaky, Halmosi, Chadwick (Ebanks-Blake 70), Fallon (Hayles 70).
Subs Not Used: Doumbe, Gosling.
Booked: Timar, Nalis, Buzsaky.
Goals: Seip 52, Fallon 59.
Att: 12,533
Ref: Nigel Miller (Durham).
~RS~q~RS~~RS~z~RS~48~RS~)