Godin captained the team on his 126th appearance to move ahead of Maxi Pereira on the all-time list, and the Uruguayans were given few problems by a Thai side that struggled against more physical opponents.
Matias Vecino gave Oscar Tabarez's squad the lead after five minutes when he headed home Nicolas Lodeiro's corner at the near post.
Gaston Pereiro made it 2-0 shortly before halftime when he rolled the ball over the line following Cristhian Stuani's low cross from the left.
Stuani put himself on the scoresheet 12 minutes into the second half when he out jumped the Thai defence to meet Giorgian de Arrascaeta's cross and power his header in.
Maximiliano Gomez added the fourth two minutes from the end with a scuffed effort to seal a scoreline that underlined the gulf between the teams.
China's woes were compounded earlier in the day as Fabio Cannavaro lost his second game in a row since taking over as head coach when the hosts slipped to a 1-0 loss to Uzbekistan.
Chinese fans had protested after seeing their side lose their opener against Thailand on Thursday and were left to witness another disappointing display in the third place playoff.
Eldor Shomurodov scored the winner for Hector Cuper's team near the end of the first half when he played himself into space behind the Chinese defence and smashed the ball past goalkeeper Yan Junling.
(Reporting by Michael Church, Editing by Christian Radnedge)
