The 29-year-old was joined by Candy Bauer, Martin Grothkopp and Alexander Schueller as he topped the podium in Altenberg after holding off two more German teams.
Fellow German drivers Johannes Lochner and Nico Walther had to settle for second and third, respectively, as Friedrich and his team finished their four runs in 3:36.09 minutes.
Lochner, who was joined by Christopher Weber, Florian Bauer and Christian Rasp, was 0.05 seconds back while Walther and his team were 0.23 seconds off the winning pace.
Bobsleigh gold sweep for Germany in Innsbruck World Cup
It is only the second time that one nation has taken the top three spots in the four-man event at the World Championships, which has been contested since 1930.
The triumph also meant Friedrich has won all four major men's title for the second consecutive season, after also taking the two-man World Cup, four-man World Cup and two-man world title.
Friedrich and Schueller take gold at Innsbruck-Igls, GB pair Hall and Cackett seal bronze
Britons Hall and Cackett claim fourth as Friedrich and Schueller take two-man top spot in La Plagne