Australia came from behind for a lucky 76-75 win over Jordan in Group A in Kayseri, while Greece pulled away for a 89-81 victory over China in Group C in Ankara.
Lithuania beat New Zealand 92-79 in Group D in Izmir, and Slovenia eased past Tunisia 80-56 in Group B in Istanbul.
Center Alex Maric had 23 points and nine rebounds for Australia, which didn't take its first lead until Maric's rebound basket made it 56-55 at the end of the third quarter.
David Andersen added 22 points, including the game-clinching two late free throws.
Zaid Abbas had 20 points for Jordan. Rasheim Wright added 16 points but he missed a layup in the final seconds and Australia took the rebound and held on for the win.
“We were very lucky to escape with a win,” Australia coach Brett Brown said. “We recognize we were fortunate to claw back and snatch a win.” Jordan, which led by as many as 11 points, did not practice or play a game for eight months after the country's Olympic committee suspended the basketball federation for “administrative and financial violations.” The team did not get together again until shortly before the worlds.
“It was a disaster,” Jordan coach Mario Palma said. “We are trying to recover from this disaster, but we are not in the shape we are supposed to be. Most of my players have not played an official game for eight months.
“Otherwise, maybe we could have beaten Australia today, we lost a big opportunity. We can play hard against any team. Maybe we can't beat them all but we can give them tough games. We can compete against any team here.” Nikolaos Zisis and Ioannis Bourousis both scored 21 points to lead Greece.
China, playing without Houston Rockets center Yao Ming who is recovering from surgery on his left foot, got within two points late in the game before Greece retook control. Yi Jianlian of the Washington Wizards had 26 points for China.
“I feel bad, it was so close,” said China guard Sun Yue, who scored 15 points.
Greece played without Antonis Fotsis and Sofoklis Schortsanitis, who were suspended earlier this week by FIBA for their part in last week's brawl in an exhibition game against Serbia.
Greece coach Jonas Kazlauskas was not happy with the performance of his team.
“They played very well on one side, I am happy for them,” said Kazlauskas, who coached China previously. “We did not play well like we played before. We had good shooting positions but we hesitated and we had problems in defense.” Linas Kleiza scored 27 points and Paulius Jankunas added 15 for Lithuania, which used a second quarter 10-0 run to take control.
Goran Dragic had 16 points and eight assists to lead Slovenia. Tunisia had only one player in double figures in its world championship debut, Radhouane Slimane with 11. The 24-nation tournament got underway on Saturday in the four Turkish cities.