The three-time European champions, who suffered a shock World Cup first-round exit last year before being relegated in the inaugural Nations League, were desperate to build on their opening qualifying win over Netherlands in March.
They took a 13th-minute lead when Sane shook off his marker and fired in from close range.
Belarus responded by forcing a fine save from Manuel Neuer, who punched Nikita Naumov's 30th-minute header over the bar for the hosts' best chance in the game.
The visitors struck again with Reus in the 62nd minute after a clever assist from Matthias Ginter and hit the post through Sane's 84th-minute header.
The result lifted the Germans to six points, three behind leaders Northern Ireland who beat Estonia 2-1 for their third win in three qualifiers.
Belarus suffered their third straight loss and are in last place, having scored only one goal.
"It was a solid performance on which we can build. We want to develop as a team," said Germany assistant coach Marcus Sorg, who replaced Joachim Low as head coach for the game. Low was briefly hospitalised days ago following a sports injury.
"The win was above everything. We had to overcome some challenges against a very defensive opponent. Overall, we did it well," said Sorg, who will also be in charge in Tuesday's qualifier against Estonia.
Earlier on Saturday, Northern Ireland came from a goal down to beat Estonia 2-1 in Tallinn.
Conor Washington cancelled out the hosts' lead through Konstantin Vassiljev's low first-half free kick and fellow substitute Josh Magennis completed the turnaround in the 80th minute to keep Northern Ireland top of the standings.
They next travel to Belarus on Tuesday.