Anton Putsila gave Belarus hope when he slotted home on the rebound after Sergey Kornilenko saw a 72nd-minute penalty saved by Hugo Lloris, but Franck Ribery settled any nerves in the home camp with France's third ten minutes from the end.
Deschamps' troops kicked off their qualification bid with a nervy 1-0 win over Finland on Friday, but looked more accomplished this evening as they took the game to the visitors, who themselves began with a 1-0 defeat in Georgia.
The French controlled the opening period and Belarus were indebted to goalkeeper Sergey Veremko for making decent saves from Mamadou Sakho and Arsenal striker Olivier Giroud inside the first 13 minutes.
Veremko again had to be alert in the 37th minute when Yohan Cabaye's inswinging corner was met with another thumping header by defender Sakho, but the goalkeeper parried the ball to safety.
Belarus finally threatened two minutes into the second half when Stanislav Dragun unleashed a shot from inside the area, but new Tottenham signing Lloris was equal to it. The breakthrough arrived in the 49th minute, though, when Ribery picked out Capoue in space in the area and the Toulouse midfielder, winning only his second cap, tucked the ball home from 12 yards.
The home side then doubled their lead midway through the half thanks to a stunning strike by Jallet, the Paris Saint-Germain midfielder also marking his second appearance for Les Bleus in style as he fired home emphatically from an acute angle.
For all France were good value for their lead, they allowed Belarus to set up a grandstand finish when they conceded a penalty inside the last 20 minutes as Mapou Yanga-Mbiwa challenged Putsila in the area. Kornilenko saw his penalty kick to the bottom-left corner saved by Lloris, but the goalkeeper was helpless as Putsila tucked home the rebound.
But the home side finally settled their jitters in the 80th minute with their third goal. Karim Benzema and Ribery combined well - as they have done so often in recent international matches - to create an opening for the Bayern Munich midfielder to prod home a chipped finish over Veremko to secure all the points.
The victory sees France to the top of the group ahead of reigning world and European champions Spain, who have only played one game so far. Belarus, meanwhile, prop up the five-team group after their winless start.