France boss Deschamps made three changes to the team that started against Bulgaria on Saturday night, with Thomas Lemar, Kingsley Coman and Olivier Giroud replacing N'Golo Kante, Alexandre Lacazette and Kylian Mbappe.
It was actually the visitors that had the first half-chance of the match in the 10th minute, but after driving into the France box, attacking midfielder Yuri Kovalev sent his effort just wide of the far post.
Giroud had France's first sight of the Belarus goal in the 14th minute, but the Arsenal forward's header from a Lucas Digne cross was always moving wide of the post.
Raphael Varane had a brilliant chance for the home side in the 18th minute after rising highest inside the away side's box, but the centre-back saw his close-range header tipped over the crossbar by Chernik. Giroud then hit the crossbar with a towering header two minutes later as Belarus started to come under intense pressure.
Seven minutes later, France doubled their lead when Griezmann fed Giroud, and the 31-year-old somehow found the back of the net after Belarus's number two Stanislav Dragun smashed the ball back against the Frenchman.
Belarus were not without their moments late in the first period, however, with Stasevich testing Lloris from distance and Anton Saroka whistling a half-volley over the crossbar.
France had been warned, and Belarus got their name on the scoresheet in the 44th minute when Saroka turned a brilliant Kovalev cross into the far corner of the net.
The first 15 minutes of the second period passed without incident, and that prompted a change from Deschamps as 18-year-old superstar Mbappe replaced the ineffective Coman.
Maksim Volodjko almost turned a Lemar cross into his own net just past the hour, before Belarus missed a golden chance down the other end - Saroka somehow firing a Aleksandr Karnitskiy cross wide of Lloris's post.
Mbappe tested Chernik with a curling effort in the 69th minute, but the score remained 2-1 entering what promised to be an end-to-end finish to the Group A clash.
As it transpired, a defeat would have still taken France to the World Cup after third-placed Netherlands beat Sweden, but the hosts were intent on wrapping up the three points, and Giroud tested Chernik from close range in the 74th minute.
Dimitri Payet also came close late on before Saroka missed for Belarus once again, but 2-1 was how it finished as France ended their Group A campaign with a narrow success.