The Pilgrims scored twice in the space of five first-half minutes, and despite Guy Branston's own goal, they held on to move four points clear of the drop zone.
He said: "It's down to the players. I thought we played really well and our first-half performance was outstanding.
"We know what is at stake and I want consistency in our game and we are starting to show that.
"To come back here and get a result is very pleasing for me but the credit goes to the players. From day one they have shown a great attitude.
"My only focus is keeping Plymouth in this division and we still have a lot of work to do but I thought we deserved this.
"We knew Chesterfield would cause us problems and they've had some good results here but although it was a sloppy goal on our part, we defended really well and it was a good team effort. Everybody worked their socks off."
- Sports & Recreation
- Guy Branston