Turkey's Ozan Tufan gave the visitors a 1-0 early lead in the fourth minute at the La Rosaleda stadium in Spain's Malaga.
Caglar Soyuncu doubled the lead with a header from a corner in the 28th minute and 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, the home side midfielder Kristian Thorstvedt was shown the red card following a serious foul play against Caner Erkin.
After starting the qualifiers with a 4-2 win over the Netherlands on Wednesday, Turkey secured their second win and collected six points in Group G so far.
In the other Group G games, the Netherlands beat Latvia 2-0, while Montenegro defeated Gibraltar 4-1.
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