The Frenchman and his team-mates responded in perfect fashion to 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.
Manager Alan Pardew and his players had found themselves in the spotlight once again in the wake of the derby disaster, but they showed genuine character to frustrate the Blues and then go for the kill when the opportunity arose.
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."
For half an hour or more, Newcastle had to fight tooth and nail to keep Chelsea at bay as the Londoners dominated possession and threatened to overwhelm their hosts.
However, apart from a 13th-minute John Terry header which crashed against Tim Krul's crossbar, they failed to convert pressure into chances and the Magpies grew in confidence as a result.
The opening goal eventually arrived with 68 minutes gone and it was Gouffran who sparked delirious celebrations among the home fans when he dived to head compatriot Yohan Cabaye's delicious 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."
But for a smart reaction save by Krul, substitute Willian might have dragged Chelsea back into the game, but Loic Remy was to have the final say when he thumped home Vurnon Anita's pull-back off the inside of the post to seal victory at the death.
Gouffran said: "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."
Pardew's master-plan proved just what was required even though, as he later admitted, his team conceded too much ground and possession to the Blues in the early stages.
However, it was based, initially at least, on sheer energy-sapping hard work, and no-one personified that more than 27-year-old Gouffran.
Pardew said: "When you look at sides like Borussia Dortmund and Bayern Munich, you say to yourself okay, your wide players nowadays need to work.
"They need to work really, really hard at the top level and you have to put him in that category. My goodness me, he worked his socks off.
"He couldn't move at the end when I subbed him, he literally couldn't even walk out. It's that kind of commitment, I think, our fans love.
"We are a working-class city and they love flair, but what they really, really want to see is that hard working grind and a day's work. My goodness me, he did a day's work today and more."
Life gets little easier for Newcastle as they prepare to head for Tottenham next weekend and another testing assignment, although they will do so with a measure of belief restored.
Gouffran said: "It's really important to have got that win for the confidence, so we move forward on the basis of that.
"We have moved out of the negative mindset we had from losing a couple of matches and we are really going to go there with fresh legs.
"We don't have a midweek game and we will go there and do as well as we possibly can."