Top seed Williams won the first set in 30 minutes on No. 1 Court against the 19-year-old Garcia who put up more of a fight than expected on a bright day at the All England Club.
The 31-year-old American, who beat Garcia en route to winning the French Open earlier this month, easily wrapped up victory against the world number 100 to take her unbeaten run to 33 matches.
Williams, a 16-times grand slam winner, will next face Japan's 42-year-old Kimiko Date-Krumm who was too wily for 23-year-old Romanian Alexandra Cadantu in a 6-4 7-5 victory.
Date-Krumm, the grand old lady of the women's singles draw, became the oldest female player to reach the Wimbledon third round in the professional era with the victory.
It is the first time Date-Krumm, ranked 84, has reached the Wimbledon third round since 1996 when she made the semi-finals.
She is the oldest woman to progress to this stage since Britain's Virginia Wade, aged 39 years, in 1985.
Former French Open champion Li Na went through the motions as she surrendered the second set meekly but recovered to win a curious match 6-2 1-6 6-0 over Simona Halep.
Halep, who had won 11 consecutive matches coming into Wimbledon, needed an injury time-out for treatment on her back at the end of the first set and the break seemed to rattle Li who committed a rash of errors in a woeful second set.
Samantha Stosur’s passage into the third round was much more straight forward with a straight-sets victory over Russia’s Olga Puchkova.
14th seed Stosur who won 6-2 6-2 will now play Germany’s Sabine Lisicki who also came through in straight sets, beating Elena Vesnina.
Madison Keys provided the only real upset early-on during day four as she sent 30th seed Mona Barthel crashing out of the All England Tennis Club with a 6-4 6-2 win.
While Laura Robson's second round clash with Mariana Duque-Marino was washed out by the weather at a wet and overcast Wimbledon.
The British number one was due to take on the unknown Colombian on Court Two but will now be upgraded to Centre Court, where she will open proceedings on Friday.
1-Serena Williams (US) beat Caroline Garcia (France) 6-3 6-2
4-Agnieszka Radwanska (Poland) beat Mathilde Johansson (France) 6-1 6-3
6-Li Na (China) beat Simona Halep (Romania) 6-2 1-6 6-0
11-Roberta Vinci (Italy) beat Jana Cepelova (Slovakia) 6-1 4-6 9-7
14-Samantha Stosur (Australia) beat Olga Puchkova (Russia) 6-2 6-2
18-Dominika Cibulkova (Slovakia) beat Maria Teresa Torro (Spain) 6-0 6-1
23-Sabine Lisicki (Germany) beat Elena Vesnina (Russia) 6-3 6-1
32-Klara Zakopalova (Czech Republic) beat Annika Beck (Germany) 7-6(5) 6-3
Madison Keys (US) beat 30-Mona Barthel (Germany) 6-4 6-2
Petra Martic (Croatia) beat Karolina Pliskova (Czech Republic) 7-6(7) 6-1
Marina Erakovic (New Zealand) beat 24-Peng Shuai (China) 7-6(6) 6-2
Tsvetana Pironkova (Bulgaria) beat Barbora Zahlavova Strycova (Czech Republic) 7-5 6-3
Kimiko Date-Krumm (Japan) beat Alexandra Kadantu (Romania) 6-4 7-5
- Sports & Recreation