Newcastle were the better side after the break and took the lead in the 68th minute when Matt Ritchie fired home after a neat flick from Perez.
Arsenal pressed hard for an equaliser but Newcastle defended stoutly to claim a fourth successive victory and condemn Arsene Wenger's side to a fifth consecutive away league defeat.
Newcastle have 41 points in 10th place with sixth-placed Arsenal on 54 -- 13 points behind fourth-placed Tottenham Hotspur. With their top-four hopes shattered, Arsenal's only route into next season's Champions League is by winning the Europa League in which they face Atletico Madrid in the semis.
While Arsenal contemplate their lowest league finish since 1995, Newcastle manager Rafa Benitez can reflect on a solid showing on their return to the Premier League.
"I think we are safe with 41 points," Benitez said. "It's a massive achievement for the players, the city and the fans. I want to congratulate everyone.
"Today we didn't play amazing football because we played an amazing team but you have to manage how you play and compete for the win. We can enjoy the win now but then we have to be ready for the next game."
Arsenal have not picked up a single point away from home in 2018 -- the only club in England's top five leagues not to do so -- but looked like ending that dire sequence when Pierre-Emerick Aubameyang clipped the ball to the far post where Lacazette thumped home a sweet volley.
Their old failings returned though and after Perez equalised with a rare Newcastle attack in the first half Ritchie punished some slipshod defending to condemn Arsenal to defeat.
"Of course it's a concern. Traditionally we are strong away from home," Wenger told a news conference when asked about his side's inability to perform away from home.
"It has a subconscious weight in our mind."
Wenger said Thursday's 2-2 draw away to CSKA Moscow in the Europa League had taken its toll on his players.
"Second half I feel some players paid a bit physically from having the game on Thursday night," he said.
"We played with good spirit but a bad result is the outcome. It's very hard to swallow."
(Reporting by Martyn Herman; Editing by Toby Davis)
