The world number 13 beat Garcia 6-2 6-3 to advance to the next round of the tournament.
Konta is the only British woman to progress beyond the second round of an Olympic singles tournament since tennis was reinstated as a sport in 1988.
Elsewhere in the competition, compatriot Heather Watson was knocked out by Ukraine's Elina Svitolina in the second round.
Watson went down 3-6 6-1 3-6 to the 15th seed.
It represents a busy day for both Konta and Watson, as they will play in the second round of the women's tennis doubles against Taiwan later on Monday, around 21:00 BST.
Other results in the competition included a 6-2 6-4 win for Czech Republic's Petra Kvitova over Caroline Wozniacki, as well as a 6-4 6-2 victory for world number two Germany's Angelique Kerber over Canada's Eugenie Bouchard.
Seventh seed Madison Keys, of the USA, also progressed to the third round, though only after a nail-biting 7-5 6-7(4) 7-6(5) win against France's Kristina Mladenovic.
Lucie Safarova retired while 2-6 down to Kirsten Flipkens.