New Toon signing Salomon Rondon scored two minutes into stoppage time to cancel out Darryl Murphy's opening goal.
However, Forest then bagged another two goals in stoppage time to seal a memorable win for the Championship club.
Despite the loss, Magpies boss Rafa Benitez wasn't alarmed by his team's performance.
"I don't agree that Forest were the better team and I'm not concerned by how we played," said Benitez.
"We did well to control the game after the first minute when we conceded. They were able to play on the counter attack.
"We did not create many chances so we need to improve in attack and keep working hard.
"It's a long season, we need it was going to be hard but we have confidence in ourselves."