Griezmann opened the scoring and then set up Olivier Giroud before the break while Belarus reduced the arrears on the stroke of halftime through Anton Saroka.
The result put France, who will take part in their sixth consecutive World Cup finals, on 23 points after 10 games, four ahead of second-placed Sweden.
Four days after a decisive 1-0 win in Bulgaria, Didier Deschamps's team were never really under pressure and avoided having to go through the playoffs, as they had to to reach the 2010 and 2014 finals.
"We did the job, our goal was to qualify first in our group," France coach Didier Deschamps told a news conference.
Belarus boss Igor Kriushenko said the hosts controlled the game.
"They had speed and they were very careful at the back," he added.
Deschamps switched from a 4-3-3 to a 4-4-2 formation with Giroud and Griezmann up front, pushing Kylian Mbappe and Alexandre Lacazette onto the bench.
France were the early aggressors but Belarus had the first clear chance when Yuri Kovalev's low angled shot whizzed just past Hugo Lloris's right-hand post in the 12th minute.
The hosts went close in the 18th when Rafael Varane's point-blank header was tipped over the bar by Sergei Chernik.
Kingsley Coman was a constant menace on the right flank and his fine cross in the 21st minute was met by Giroud, whose header crashed onto the bar.
The hosts were rewarded for their efforts six minutes later, however, when Griezmann beat Chernik from close range after a Blaise Matuidi through ball tore the Belarus defence wide open.
They doubled their tally six minutes later as another through ball, this time from Griezmann, was collected by Giroud in the area and the Arsenal forward clinically slid it past Chernik.
It was Giroud's 28th goal for France.
France's concentration levels dipped, however, and they were punished on the stroke of halftime when Saroka's cool finish allowed the visitors to grab a route back into the game.
Yet France maintained control in the second half as Mbappe came on as a substitute for Coman, but made little impact.
Belarus threatened on the break and Deschamps, sensing danger, replaced Griezmann with the more defensive Moussa Sissoko.
From then on, the hosts were just content to keep their foot on the ball and look to hit their opponents on the break.