Tonga finished Saturday's match with 14 men after back-rower Siosiua Moala received a second yellow card in the 68th minute, which became a red. Moala was penalised on both occasions for joining a maul on the side and collapsing.
Fiji won a scrappy and ill-tempered match in Suva for their 11th win over Tonga in their past 12 meetings.
Later in Sendai, hosts Japan opened their campaign with a statement performance, scoring eight tries to two in a 57-15 win over Canada, who beat the United States 34-20 in their first match of the tournament.
Back-rower Amato Fakatava and winger Kippei Ishida crossed for doubles and Warner Dearns scored a try in his first outing as Japan skipper.
"Canada really showed up in the first half and we were under a lot of pressure. I've got to thank the boys for coming out in the second half and putting up a good fight," Dearns said.
"I'm really happy to win my first game as captain."
Fakatava scored the opening try after only three minutes. But the visitors scored through Sion Parry to level at 10-10. Dearns' try in the 38th minute allowed Japan to go to halftime with a seven-point lead.
The hosts took 14 minutes to score their first try of the second half through Fakatava but then ran riot with tries to fullback Sam Greene, back-rower Ben Gunter, centre Tomoki Osoda and Ishida, who scored twice in the last few minutes.
Tonga opened their campaign last weekend with an impressive 30-16 win over Samoa and started strongly on Saturday with an early try to scrumhalf Augustine Pulu.
Fiji took the lead for the first time with a superb long-distance try finished by former All Blacks centre Seta Tamanivalu.
Winger Kalaveti Ravouvou crossed during Moala's first absence in the sin bin, and by halftime Fiji led 17-10.
Captain Tevita Ikanivere scored in the 63rd minute from a cross-kick by Caleb Muntz and Taniela Rakuro added Fiji's final try five minutes later in a goal-line scramble.
"We didn't start well, but I'm grateful for the boys showing great spirit and getting the win," Ikanivere said.
"It was quite tough: big bodies against big bodies, and there was a bit of blood on the field."
In the third and final preliminary round on September 6, Fiji and Samoa play in Rotorua, New Zealand, and the United States host Japan in California.
Denver is hosting the semi-finals and fifth-place playoff on September 14 and Salt Lake City the third-place playoff and final on September 20.
