Twelve months ago Robson followed up her defeat of Kim Clijsters by beating former French Open champion Li to reach the fourth round of a grand slam for the first time.
Rain held up Robson and Frenchwoman Garcia for almost five hours but the 19-year-old British number one produced a very composed display to win 6-4 7-6 (7/5), saving two set points in the second set.
Robson said: "I'm very happy. I thought I played fairly well. I didn't start off on her service games too well. I don't think I won a point until the third time around (it was actually the fourth).
"It was good to just stick with her, and then I took my chances when I had them.
"I was really happy with my serve, especially my second serve. She made a lot of mistakes off that, so I was just trying to spin it as much as possible. It definitely went well."
The only real moment of concern came at the end of the first set when Robson, who missed her previous three tournaments with a wrist tendon injury, called for the trainer.
She took some painkillers and had her right wrist retaped, and Robson was again keen to play down the issue after the match.
The teenager insisted the painkillers were precautionary, and it would obviously be much more of a problem if it was her left wrist, but it is clearly bothering her.
Asked if it would be an ongoing factor, Robson said: "I think I'm playing my forehand well enough for it not to be."
Garcia was tipped as a future world number one by Andy Murray when she almost upset Maria Sharapova at the French Open two years ago but it is Robson who has made the greater strides so far.
The British teenager is seeded at a grand slam for the first time and looked good in her first-round win over Lourdes Dominguez Lino.
The only real improvement she needed to make was in her serving after throwing in eight double faults in that match, and it was mission accomplished here.
Both players possess big serves and used them to great effect - Garcia did not drop a point in her first three service games, sending down one ace at 114mph.
When Robson did get the ball back in play, she was having a lot of success, her greater weight of shot helping her dictate a lot of the rallies.
She could not capitalise when she had Garcia at 0-30 in the eighth game, but two games later she put pressure on the Frenchwoman and won four points in a row to take the set.
Break points were just as scarce in the second set right up until Robson served her first double fault of the match to lose her serve in the 11th game.
That gave Garcia the chance to serve for the set, and she had two chances to take it but threw in a double fault of her own and Robson blasted her way to a break back.
Robson then won six points in a row in the tie-break to lead 6-2, and took her fourth match point.
The 30th seed also reached the fourth round at Wimbledon and is happy that she is now showing the form against lower-ranked opponents that she has often reserved for the bigger names.
She said: "I thought, starting from Wimbledon, I felt like I was winning the matches where I was supposed to win them, especially my second and third rounds there. That's what I've done here so far.
"It's definitely a big match in the third round against Li Na. It's going to be a tough one."