The teenager was a doubt ahead of the tournament after picking up a leg injury during an event in Mexico just two weeks ago.
Despite this, she was able to recover in time and put on an impressive performance during her 6-1 3-6 6-1 victory over Garcia.
The win was timely considering Raducanu's difficult start to the season. The Brit has faced problems with Covid-19, blisters and early eliminations but appears to be returning to form.
The 19-year-old was in full control of the opening set and took it inside 27 minutes, dropping just one game in the process.
Her French opponent fought back in the second and won 6-3 to take the match to the final set.
However, Raducanu showed her class and secured her place in the third round with a 6-1 win in set three.
The Brit will now take on Croatia's Petra Martic in the next round of the BNP Paribas Open.