The midfielder proudly wore the armband and completed a full shift as his side raced into a 3-0 lead at half-time at Seoul World Cup Stadium with goals from Darwin Nunez, Giorgian de Arrascaeta and Guillermo Varela.
Nunez headed home his second and Uruguay's fourth in the second half before Lee Kang-in scored a late consolation for the hosts.
That was Rodri's 78th cap - his former team-mate Heung-Min Son captained South Korea.
Meanwhile, George Jobling and Toju Wellspring came off the bench as England Under-17s began the first of three matches in Germany with a 2-1 win against Israel on Monday. Mikel Jack was an unused substitute. The Young Lions next face Venezuela on Thursday.
Ted Evans started and completed a full shift as Wales Under-17s beat Northern Ireland 2-0 in a friendly at Oliva Nova, Spain.
Monday night's action