The former Manchester United winger now has four goals and three assists in all competitions for the the Istanbul giants.
Nani has been directly involves – providing an assist or scoring – in five out of the Canaries last six goals in all competitions.
The Portuguese international curled the ball around Bursaspor keeper Mert Günok on 20 minutes to put his side ahead.
Nani’s former Manchester United teammate Robin van Persie scored the Canaries second goal of the game on 79 minutes to take back all three points.
The Portuguese international joined Fenerbahçe on a £4.2 million move from United over the summer transfer window signing a three-year deal with the Istanbul giants.
The win saw Fenerbahçe move three-points clear at the top of the table with 13 points after five games.