Gael Clichy scored the opening goal in the 49th minute and 19-year-old midfielder Garcia added a second on 67 minutes before the Swans, through Gylfi Sigurdsson, pulled one back in injury-time.
The win against the Swans was City's ninth consecutive win under Guardiola who felt Garcia and Fernando performed admirably in their midfield roles.
"(Garcia) played good, and I want to congratulate the young players tonight. They played good," said Guardiola, who also handed game time to academy stars Tosin Adarabioyo, Brahim Diaz and Angelino.
"Fernando made an amazing effort, because he had been injured for the last two weeks. He played a fantastic game."