The Stade de France fell silent prior to kick off in memory of the 130 civilians that lost their lives in the Paris terror attacks, two days before the first anniversary of the atrocity.
Sweden had threatened an upset when Emil Forsberg put them ahead nine minutes into the second half, before Pogba and Payet hit back to seal three points for Les Bleus.
Forsberg’s opener was spectacular, firing a 25-yard free kick past Hugo Lloris.
Pogba responded just four minutes later, heading home Payet’s free-kick, before the West Ham man crowned an impressive display with a goal of his own 25 minutes from time.
French president Francois Hollande, who was present last year as France played Germany during the terror attacks, attended the match.
“We have to remember. One year ago, almost to the day, we were here for a friendly game and three bombs were detonated, with one man being killed,” Hollande told French TV.
“We have to remember there were 130 people who died and hundreds of others who were injured. For them and for those who survived we must remember.”
Some 1,200 stewards and 400 police officers were on duty at the match but no incidents were reported.