Germany struggled for creativity at the Borisov Arena despite a star-studded line-up, but Sane's first-half strike set up the Group C victory.
Manchester City forward Sane — linked with a move to Bayern Munich — finished coolly to make it 1-0 and Reus struck to settle matters after the interval.
Aleksandr Gutor made a smart block to keep out Serge Gnabry's drive as Germany started well, but the Belarus goalkeeper was beaten in the 12th minute.
Joshua Kimmich slipped a pass through to Sane, who cut inside a defender to smash home.
But Belarus rallied and Lukas Klostermann made a superb block to deny Stanislav Dragun a clear strike, with Manuel Neuer tipping Nikita Naumov's header over from the resulting corner.
Despite not getting out of second gear, Germany doubled the advantage in the 62nd minute.
Matthias Ginter bisected the Belarus back line with an incisive pass from the right and Reus burst into the box and slammed his finish past goalkeeper Gutor.
Germany pushed to extend its lead in the closing stages but when Ginter delivered a fine cross into the box Sane saw his header bounce back off the foot of the post.
Germany continues its qualifying campaign at home to Estonia in midweek, with Belarus hosting Group C leader Northern Ireland on the same day.