Fifth seeded Tsonga, a Queen's runner-up in 2011, won the first set after securing the key break at the end of a marathon sixth game.
Tsonga's strong start to his grass-court campaign was the perfect way to erase the painful memory of an embarrassing first round exit against unheralded Argentine Renzo Olivo on the clay at Roland Garros.
That was the first time Tsonga had lost in the opening round of a Grand Slam in 35 appearances, but there was no hangover in the west London sunshine as he brushed aside fellow Frenchman Mannarino in just 66 minutes.
Fifth seeded Tsonga, a Queen's runner-up in 2011, won the first set after securing the key break at the end of a marathon sixth game, despite a worrying tumble when he slipped after making a shot behind the baseline.
Shaking off that injury scare, the 32-year-old won seven games in a row and even found time to high-five a ball girl as he avenged his loss to Mannarino in Monte Carlo earlier this year.
Tsonga, who has won titles in Lyon, Marseille and Rotterdam in 2017, will play Gilles Muller or Nikoloz Basilashvili in the second round of the Wimbledon warm-up event.
Grigor Dimitrov is another who excels on grass and the Bulgarian world number 11 cruised into the second round with a 6-3, 6-1 win against Ryan Harrison of the United States.
Dimitrov is the only player other than reigning champion Andy Murray to win the Queen's title in the last four years and he looks in the mood to push the world number one for the crown this year after crushing Harrison in 54 minutes.
The 26-year-old, who made the Australian Open semi-finals in January, faces French qualifier Julien Benneteau or British wild card James Ward in the last 16.