Plymouth took a 44th-minute lead when the ball ricocheted off Minstermen left-back Jamal Fyfield and in, helped over the line by Rhys Griffiths following Luke Young's corner from the left.
Substitute striker Nick Chadwick claimed the second goal in the 89th minute after Michael Ingham made a superb save to keep out Young's thumping shot from 18 yards after Mark Molesley's defence-splitting run.
Fletcher said: "It was a big win and good to keep the clean sheet as well. We completely dominated the game. I don't think York had a shot on target.
"It was not anything majorly different to what we have been doing for the last couple of months really just that we got the rub of the green and a couple of goals, which the performance deserved.
"We have had it so often this season where we are in control and something falls to them and it goes into the back of the net.
"You are always worried about that, especially at 1-0. But thankfully we got that second goal just to ease all the nerves around the place and fully deserved it.
"We saw the game out and did what we needed to do. York are a capable side but we did well against them, and didn't let them play.
"I am not sure whether Rhys is claiming the first goal or not, I will have to look at it again.
"It looked a little bit of a melee and then it has gone in and possibly that is the sort of luck that we have not been getting lately. It's something that has not gone for us in previous games."
- Sports & Recreation