Matthias Ginter scored the opener four minutes from half-time, before midfielders Leon Goretzka and Toni Kroos – who netted a brace – completed the scoring to move top of Group C, two points clear of Holland.
Northern Ireland's failure to win at home to the Dutch meant the three points were enough for Joachim Low's side to progress to next summer's tournament.
Germany were dominant from the outset but had to wait until the 15th minute to have their first real chance on the Belarus goal, when Ginter forced Aleksandr Gutor into a save low to his left.
Kroos and Serge Gnabry fired narrowly wide as Germany pushed for the opening goal, but they survived a major scare at the other end when Manuel Neuer denied Igor Stasevich with a brilliant save in the 40th minute.
The home side finally made the breakthrough a minute later and in superb style, as centre-back Ginter produced a stunning backheel finish to Gnabry's enticing low cross.
It took only four minutes after the restart for Germany to double their lead with a well-executed set-piece, which was finished off by Bayern Munich midfielder Goretzka.
Kroos took a quick corner low into the penalty area in the direction of Ginter at the near post, only for the Borussia Monchengladbach defender to step over the ball for Goretzka to fire into the bottom left corner.
Kroos went from provider to goalscorer in the 55th minute with a well-taken effort from the edge of the penalty area that left Gutor rooted.
Despite trailing 3-0, Belarus then burst into life, with Yuri Kovalev heading wide before the visitors were awarded a penalty for a foul by Robin Koch.
However, Neuer preserved his clean sheet by guessing correctly to save Stasevich's spot-kick.
Kroos netted the fourth and final goal late on as the Real Madrid midfielder produced a great turn in the Belarus penalty area before cutting onto his left foot and drilling into the bottom right corner.