The Magpies bounced back from their 2-1 reverse at the Stadium of Light and their midweek Capital One Cup exit at the hands of Manchester City to see off Jose Mourinho's title favourites 2-0 at St James' Park.
Asked how tough the week had been, Gouffran said: "It was really, really difficult. It was an exhausting match for us against Manchester City. We lost in extra-time, so we had to play that much longer.
"Coming off the back of a derby defeat, we were very disappointed. We know we could have done a lot better in the week.
"It was disappointing to have lost it and we had to go out there and show a really different side of ourselves on the pitch and really make it up to the fans, and we did that.
"At the beginning of the match the manager told us we had to stay solid as a defensive unit - even the attackers had to make sure they stayed solid in our half.
"In the second half Chelsea had to come forward, they needed to try to score and that's when we were able to go forward and take our chances.
"We were fantastic from the first minute until the very end. We were really solid defensively as a unit and we took our chances when we needed to, and it has given us a really good confidence boost."
Gouffran opened the scoring for Newcastle in the 68th minute when he dived to head Yohan Cabaye's free-kick past the helpless Petr Cech.
The former Bordeaux player said: "It was magnificent. The fans made one hell of a noise.
"I really just wanted to go and slide. I hurt my knees a little bit and got some grass burns, but it was really nice and a wonderful feeling."