The game's dominant player, Williams, who lives an hour drive away from the Crandon Park complex, has yet to put her stamp on her home tournament, advancing with a pair of laboured wins over Yaroslava Shvedova and Garcia.
The hard-hitting Frenchwoman showed no fear, slugging it out with the 17-time grand slam winner for more than two and a half hours before Williams ended the fight with a blistering forehand winner.
"I really gave myself a tremendous amount of trouble out there," Williams told reporters. "Granted she played great but I made so many errors. I hit so short.
"I just have to do better."
A more unsettling sight for tournament officials has been the large swaths of empty green seats, the hometown girl and the biggest draw in women's tennis unable to attract a full house to either of Williams' centre court matches.
Meanwhile, Williams' serve seems to have deserted her, the muscular American unable to find her mark against Garcia while firing seven double faults.
A minority owner in the National Football League Miami Dolphins, a smiling Williams stepped out onto centre court dressed in the orange and turquoise colours of her team earning the approval of the half empty stadium.
But the smiles did not last long, a misfiring Williams spending most of the match gesturing, scowling and shouting at herself for a string of miscues.
"It's important to stay positive," said Williams. "Obviously I wasn't at my best. I had 40 something errors. It's not the way to play professional tennis. Maybe amateur.
"On the professional tour you have to do a little better than that, so hopefully I can, in the next few matches, to do better."
The contest got off to an uneven start, Williams breaking Garcia three times with the Frenchwoman countering with two breaks of her own.
In contrast, the rest of the match would produce just two breaks, Garcia breaking Williams to take the second set and the defending champion breaking the Frenchwoman to open the third.
"I just try to forget it's Serena Williams, to forget that she won how many Grand Slams and just be me and just play," said Garcia, now 0-3 against Williams. "If I want to win a match like this, I have to play and don't think of my opponent, what she is doing in the past but just be focused on what she's doing now and how I play now."
In other action, fifth seeded German Angelique Kerber raced into the fourth round with a 6-0 6-2 demolition of Bulgarian Tsvetana Pironkova while ninth seed Sara Errani of Italy was stopped 6-3 2-6 6-4 by 23rd seeded Russian Ekaterina Makarova.
The morning session featured an intriguing clash between 12th seeded Serb Ana Ivanovic and Italian Flavia Pennetta, who arrived in Miami riding the momentum from a victory at the BNP Paribas Open at Indian Wells.
Ivanovic, a former French Open champion, ended Pennetta's run with 6-4 6-3 victory setting up a fourth round meeting with 2011 Wimbledon winner Petra Kvitova, the eighth seed advancing with a no-nonsense 6-3 6-4 win over Croatian Donna Vekic.
Belgian Kirsten Flipkens moved onto to the fourth round in a walkover when 14th seed Sabine Lisicki withdrew due to the flu.
Results from the Miami Women's Singles Round 3 matches on Saturday
Serena Williams (U.S.) beat Caroline Garcia (France) 6-4 4-6 6-4
19-Kirsten Flipkens (Belgium) beat 14-Sabine Lisicki (Germany)WO
8-Petra Kvitova (Czech Republic) beat Donna Vekic (Croatia) 6-3 6-4
23-Ekaterina Makarova (Russia) beat 9-Sara Errani (Italy) 6-3 2-6 6-4
12-Ana Ivanovic (Serbia) beat 20-Flavia Pennetta (Italy) 6-4 6-3
5-Angelique Kerber (Germany) beat Tsvetana Pironkova (Bulgaria) 6-0 6-2
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