Wijnaldum struck twice in the first half, either side of Dieumerci Mbokani's equaliser for the visitors at St James' Park.
Ayoze Perez netted Newcastle's third, only for Nathan Redmond to pull one back immediately for Norwich, but the second period belonged to the home side.
Mitrovic's strike restored the two-goal advantage, and Wijnaldum completed his hat-trick with a header before rounding off the scoring with a deflected effort as Newcastle won their first Premier League game of the season at the ninth attempt, and the midfielder was hailed by his team-mate after the game.
"Gini [Wijnaldum] showed a bit of magic today. He will score more goals. I am pleased for him," the striker told Sky Sports.
"I enjoyed the goal a lot. We played the perfect game. After a few bad games we showed how to play football.
"I am very happy here and hope I will score more goals for Newcastle. From Tuesday onwards we will get ready for Sunderland - I hope we will play like this."