Fabian Schär netted twice - becoming the first Newcastle defender since Philippe Albert in 1996 to bag a league brace for the Magpies - before Pérez added gloss to the scoreline in injury time, completing an incisive attacking move as United leapfrogged their opponents in the Premier League table.
Before the crunch clash, Newcastle lay one point adrift of 17th placed Cardiff and, after a tense opening 20 minutes, Pérez highlighted the significance of Schär's first ever goal in a black and white shirt - a fine solo effort from the Swiss international - on their way to claiming three crucial points.
"It was a very important win," Pérez told nufc.co.uk. "We knew this game was crucial for us and, as I said after the match against Blackburn, we had to be out together as a team. It was going to be like a final - a massive game - and, thankfully, we managed to take the three points. There is still a long way to go but we are happy with the win and we now need to carry on in this way.
"The first goal was the most important out of the three. I think before half time the game was quite tough with a lot of long balls and not much football being played but with the goal, we gained more spaces in the second half and took advantage of our opponents to manage the game as well as we could.
"I was happy to score towards the end and we won by three goals. It was a great performance and everyone is pleased with the result. The importance of this game was very high with the position we were in before the game. We did our job well so the feeling to score the third goal late on, realising you have won the game, is great."
After Rafa Benítez's side recorded their most convincing win of the campaign, Newcastle took their tally to seven goals for the week, following the Magpies' 4-2 FA Cup win at Blackburn on Tuesday.
The Spanish forward, who also got his name on the scoresheet in the closing stages of extra time at Ewood Park, insisted his determination to grab his third Premier League goal of the campaign was a major factor.
"You have to believe you can get a chance to score at any time," Pérez added. "I made one of the last runs going into the counter-attack, making the movement to score. It is all about belief and making sure we can create as many chances as possible. That is the mentality we need to have to make the opposition feel uncomfortable and make St. James' Park a tough place for teams to come to.
"I'm looking for another goal. That is my focus going into the next game, trying to get chances and score again. That is what it is all about as a striker so I'm trying to improve my numbers and if I score, that is good for the team which is the most important thing."
