Casper Ruud will make his debut at the ATP Finals after clinching his spot on Thursday at the ongoing Paris Masters.
The five-time champion in Paris/Bercy will play his first tournament since falling to Daniil Medvedev in the final of the US Open.
Jannik Sinner has moved into the top-10 of ATP rankings after he overcame Frenchman Gael Monfils to defend his Sofia Open title.
Rublev, ranked No.5 in the world, claimed the first set with a scorching 117 mph ace before Norrie, ranked No. 28, rebounded to force a decisive third set to reach his fifth final of the year.
Denis Shapovalov and John Isner beat Team Europe's Alexander Zverev and Berrettini to earn Team World's lone point on the first day.
Casper Ruud moved past the 71st ranked Gilles Simon of France 6-4, 7-6(4) to reach the second-round at the Mallorca Championships.
The second-seeded Shapovalov beat Pablo Cuevas 6-4, 7-5 and the third-seeded Ruud won 6-3, 6-2 against Pablo Andujar as the two 22-year-olds both defeated 35-year-old opponents.
Struff made his first tour final after ending a seven-match losing run in semifinals by stopping in-form qualifier Ilya Ivashka 6-4, 6-1.