First-half goals by the diminutive forward and 19-year-old debutant Kyriakos Papadopoulos put Fernando Santos's team firmly in charge at the Georgios Karaiskakis stadium.
Michael Mifsud pulled one back for Malta just after half-time but Fetfatzidis calmed the home side's nerves with his second of the night just after the hour to seal the three points.
Greece regained top spot after Croatia briefly led the group with a 2-1 home win over Georgia on Friday. Greece have 14 points with Croatia a point behind also after six matches while Israel are third on 10 from seven following a 2-1 win in Latvia.
The hosts began brightly in Piraeus and were ahead after just eight minutes, Fetfatzidis tapping home after a precise low centre from his Olympiakos team-mate Vassilis Torossidis.
Malta struggled to get hold of the ball as Greece continued to press forward, and the home side were 2-0 up in the 26th minute when Kyriakos Papadopoulos surged into the area and headed home captain Giorgos Karagounis' free-kick.
John Buttigieg's Malta team got back into the game nine minutes after the break when Mifsud slotted home after some sloppy defending and their substitute Andrew Cohen was unlucky when his long-range drive cannoned back off the left post.
But the game was put to bed by Fetfatzidis after 64 minutes, the talented winger slotting into an empty net after goalkeeper Andrew Hogg had parried Dimitris Salpingidis's cross.
The result means Santos is undefeated in 10 matches as Greece coach since taking the helm after the 2010 World Cup.
Greece visit Israel in their next qualifier on September 2 when Croatia travel to Malta.
