Garcia, ranked 55th in the world, defeated the British No. 1 and reigning US Open champion in 86 minutes on Centre Court.
The defeat means it's three second-round losses in a row for Raducanu, 19, in this year's Grand Slams. It has been a tough year for Raducanu after she stormed to her remarkable US Open triumph in 2021. She's had to cope with several injuries, while the start of the season was disrupted by testing positive for COVID-19 in December.
"There's no pressure. Like, why is there any pressure? I'm still 19. Like, it's a joke. I literally won a Slam,'' Raducanu said. "Yes, I have had attention. But I'm a Slam champion, so no one's going to take that away from me. Yeah, if anything, the pressure is on those who haven't done that.''
Raducanu entered this year's Wimbledon having played just seven games of tennis on grass this year, as she retired in the opening round of Nottingham after suffering a side strain. It was touch and go as to whether she'd be fit for Wimbledon, but she came through to face Alison Van Uytvanck on Monday, and in her first-ever match on Centre Court, she won in straight sets.
But Garcia, 28, proved to be too much for Raducanu, breaking her serve twice en route to winning the first set. Garcia then broke Raducanu's serve to make it 3-2 in the second, only for Raducanu to break back in the next game. But the parity did not last long as Garcia broke Raducanu's serve again in the following game and then held her own to go 5-3 up.
The crowd continued to get behind Raducanu as she went to serve to stay in the match, but Garcia needed only one match point to book her spot in the second round as she broke Raducanu's serve for the fifth time.
For Garcia, this triumph means she's started her Wimbledon single's campaign with back-to-back victories over British hopefuls, after she needed three sets to get past Yuriko Miyazaki on Monday in the opening round. Garcia, whose best record at a Slam was her quarterfinal finish in the 2017 French Open, now faces No. 33 seed Shuai Zhang in the third round on Friday.
For Raducanu, attention now shifts to the hard-court season as she builds to her defense of the US Open title.
"Going back to New York, it's going to be cool because I have got a lot of experiences playing on big courts, playing with people in the stadium, playing with the spotlight on you,'' Raducanu said. "I don't mind that. I mean, for me, everything is learning. I'm embracing every single moment that is thrown at me.''
Kontaveit has never reached the fourth round at the All England Club, the only one of the four major tournaments in which she has failed to get that far. She was making her eighth appearance at Wimbledon.
It was Kontaveit's first match on grass this year.
Kontaveit, 26, said she had COVID-19 in recent months and has struggled to get her energy back.
"I had it a couple, two months ago, I think, or something like that. Then I tried to come back very quickly. I started training. It was low intensity, but I was still training every day. I think that was where I went wrong," she said. "Just thinking back at it, I probably should have given myself more time to recover.''
Among the winners were No. 6 Karolina Pliskova of the Czech Republic, who beat Tereza Martincova 7-6 (1), 7-5 in a match that started Tuesday, and No. 8 Jessica Pegula of the United States, who defeated Croatia's Donna Vekic 6-3, 7-6 (2).
Information from The Associated Press was used in this report.