The 28-year-old who completed an 18-month loan from Chelsea on Friday was introduced as a 66th-minute substitute in the encounter that saw the Yellow Canaries grab their fourth league win of the season.
Moses replaced Algeria’s Yassine Benzia as Mehmet Ekici’s brace and Mehmet Topal’s effort guided the hosts to victory in a five-goal thriller.
The triumph saw Fenerbahce climb to the 14th spot in the Turkish top-flight table with 20 points from 19 matches – two points above safety.
For Moses, he was thrilled to see the atmosphere created by the club’s ‘amazing’ supporters on his Turkish top-flight bow.
The Nigeria international will hope to push Ersun Yanal’s side to victory again when they host Goztepe for their next league fixture on Friday.