Ozan Tufan gave the visitors an early lead in the fourth minute at the La Rosaleda stadium in Spain's Malaga. Caglar Soyuncu doubled the gap with a header from a corner in the 28th minute. The first half ended 2-0.
Tufan scored his second goal with a superb long-range strike in the 59th minute to make the score 3-0. In the 80th minute, Norway's midfielder Kristian Thorstvedt was shown a red card after a serious foul on Caner Erkin.
After starting the qualifiers with a 4-2 win against the Netherlands on Wednesday, Turkey secured their second win and collected six points in Group G. In other Group G games, the Netherlands beat Latvia 2-0 and Montenegro defeated Gibraltar 4-1.
In a post-game interview, Turkey's manager Senol Gunes said he is proud of the team's game and his players were smart, disciplined and patient against Norway.
"We played against the strong team, Norway, and we beat them. We are happy. We won and we did everything right."
"We knew the strengths of our opponent. We took good advantage of their weaknesses," said Gunes.
He added that the successful counter attack plan turned the game in Turkey's favor.
Turkey's president congratulated the team for their victory.
Recep Tayyip Erdogan spoke with Gunes and captain Burak Yilmaz by phone.
"I congratulate all our footballers. This was a very sharp team. It is really very good, you gave the lesson of team football," he said.