In an impressive performance in Berlin, CSKA defeated hosts Alba 84-68, leading at every change to overhaul reigning Euroleague champions Maccabi Electra at the top of Group B's standings.
And in Russia, Nizhny edged out Dinamo Banco di Sardegna Sassari 88-86.
With new coach Dimitris Itoudis in charge of CSKA for his first continental fixture, the Russians jumped out to an 8-2 lead early in a sign of what was to come throughout the match.
The visitors led by four points at the end of the opening quarter and six at half-time, extending their lead further in the second half to eventually win by 16.
Sonny Weems and Milos Teodosic were key to CSKA's victory with both scoring 15 points and notching five assists, while Sasha Kaun top-scored with 16 and added nine rebounds.
For Alba, Reggie Redding (11 points) was the only player to reach double figures, while Jamel McLean (nine points, seven rebounds) battled hard.
Nizhny had to come from behind to win their first Euroleague match as they trailed Italy's Dinamo Sassari by 11 points at the end of the first quarter.
Dinamo Sassari led 9-0 in the second minute and stormed away to a 26-7 lead with three minutes remaining in the opening term but the home side fought back to trail 26-15 at the first break.
With Tarence Kinsey (17 points, seven rebounds) firing for Nizhny, the hosts overhauled their Italian opponents in the third quarter to lead 66-61 with a period to play, and although Dinamo Sassari had a chance to win the match in the closing seconds, the home fans were able to celebrate victory.
Artsiom Parakhouski (16 points, eight rebounds) and Trey Thompkins (16 points) were critical to Nizhny's triumph, while David Logan (17 points, five assists) and Jerome Dyson (17 points) were the visitors' best players.
The win took Nizhny to third in Group A behind Real Madrid and Anadolu Efes on points difference.
Madrid - Group A-leaders and last season's runners-up - started their Euroleague campaign with an 80-71 win over Zalgiris of Lithuania.
Madrid's arch-rivals Barcelona defeated Bayern Munich 83-81 in Group C, where they trail Panathinaikos and Fenerbahce Ulker, who trumped Turow Zgorzelec 84-77 and EA7 Olimpia Milano 77-74 respectively.