Ginter broke the deadlock in the 41st minute with a clever backheel, provided a dummy which allow Leon Goreztka to score the second and the pass for Toni Kroos to add the third.
Germany goalkeeper Manuel Neuer saved a penalty from Igor Stasevich in the 75th minute and Kroos added a fourth.
Group C leaders Germany, with 18 points, qualified with one match to spare along with the Dutch, who are two points behind. Northern Ireland are on 13 with one match each to play.
Belarus could still qualify through the Nations League play-offs in March.
Croatia qualified for Euro 2020 after second-half goals from Nikola Vlasic, Bruno Petkovic and Ivan Perisic inspired a comeback 3-1 home win over Slovakia in a pulsating Group E qualifier on Saturday.
The result left the Croatians on 17 points from eight games as they completed their campaign, with three sides behind them still in contention for next year's 24-nation tournament.
Second-placed Hungary (12 points) visit third-placed Wales (11 points) on Tuesday in a dogfight for a top-two finish where a win would see either through.
David Alaba’s early goal and a snap effort from Stefan Lainer in the second half ensured Austria qualified for next year’s European Championship with a 2-1 win over North Macedonia on Saturday.
It is a second successive qualification for Austria and will be only their third appearance at the finals, having also been co-hosts in 2008.
The victory kept Austria second in Group G, behind already qualified Poland, who won on Saturday in Israel, and left North Macedonia hoping for success in the playoffs to have any chance of also participating in the finals.