It was the perfect answer to their 6-1 defeat at Manchester City in their last match and sets them up perfectly for next week's derby at arch-rivals Sunderland, who are now bottom and the only Premier League team without a win.
The victory lifted Newcastle to six points and 18th place, leaving Aston Villa (four points) and Sunderland (three) below them in the relegation zone. Norwich, promoted last season, slipped one place to 16th on nine points.
"We needed it. We have had a few games when we have played good, but not got the points or only one point," Wijnaldum told Sky Sports.
He became the first Newcastle player to score more than three goals in match since Alan Shearer grabbed five against Sheffield Wednesday in 1999. "I've done it before for Feyenoord against FC Groningen," he said with a smile.
United manager Steve McClaren, who insisted before the game that Newcastle's season was going to "start today" said he was relieved the win had finally come.
"We have had to be patient, but I am pleased for the supporters and the players, it's been tough, it's been hard. They deserved that. I am very proud of them.
"We showed our strengths, what we are very good at, but we also showed some of our weaknesses in controlling the game and conceding the two goals."
DEFENSIVELY POOR
Although Newcastle were convincing winners in the end, Norwich made it hard for them while the score remained at 3-2 for half-an-hour.
But Norwich manager Alex Neil told Sky: "I thought we looked dangerous going forward but as a group defensively we were really poor."
The first five goals came in 20 minutes after Wijnaldum opened the scoring in the 14th minute with Dieumerci Mbokani Bezua equalising six minutes later.
Wijnaldum headed Newcastle 2-1 ahead after 26 minutes with Perez making it 3-1 in the 33rd before Norwich came right back to make it 3-2 with a Nathan Redmond volley a minute later.
Norwich continually threatened another equaliser after the break before Newcastle wrapped up their long-awaited victory with two goals a minute apart.
Mitrovic chested down and volleyed home, Shearer-style, to make it 4-2 after 64 minutes. Wijnaldum headed home to complete his hat-trick a minute later before scoring his fourth with a thunderous long-range strike after 85 minutes.
(Reporting by Mike Collett, editing by Alan Baldwin and Ken Ferris)
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