The top seed needed just over an hour to move past the French teenager 6-3 6-2.
The American will face 42-year-old Japanese player Kimiko Date-Krumm in the next round.
Read how all the action unfolded below.
12.56pmGood afternoon. The players are due to head out to Court One at 1pm this afternoon, so action should be getting underway in around 10-15 minutes' time.
12.59pmSerena Williams needs little introduction. The world number one is the defending champion at this tournament, having secured her fifth title at SW19 last year. In total, she has 16 Grand Slam singles titles, 13 doubles titles, four Olympic gold medals and 52 WTA titles.
1.02pmCaroline Garcia is still a relative newcomer, having turned pro in 2011. This is the first time that she has made the main draw at Wimbledon, having bean beaten in the qualifiers for the last two years. In six Grand Slam appearances, she has never made the third round.
1.04pmThe pair have only played once before, and that was at the French Open last month. Williams dominated her 19-year-old opponent, wrapping up the match 6-1 6-2.
1.07pmThe players have just come into the court to start their warm-ups for today's match. Following Maria Sharapova's and Victoria Azarenka's exits from Wimbledon yesterday, it's difficult to see who could present a challenge to Williams at this tournament.
1.10pmWe now know that the winner of this match will face 42-year-old Kimiko Date-Krumm in the next round, following her straight-sets win over Alexandra Cadantu this morning. The Japanese player is a former semi-finalist at Wimbledon, having made the last four in 1996.
1.14pmOver on Centre Court, former US Open champion Juan Martin del Potro has just got his second-round match underway against Jesse Levine. You can also follow that match with Sports Mole this afternoon.
1.16pmThe umpire has just announced that Garcia, who is currently ranked 100 in the world, won the coin toss and has chosen to serve first.
1.17pmThe players have finished their warm-ups, and they're ready to get the match underway.
Williams *0-1 GarciaGarcia makes a confident start, wrong-footing Williams at the baseline before coming into the net to smash a volley past the American. She wraps the game up with an ace, followed by a forehand winner into an empty court.
Williams 1-1* GarciaWilliams gets her big serve working for her, with Garcia failing to get her first two returns in, before the top seed secures her first ace of the match. Another powerful delivery from the American is too much for the 19-year-old to control, giving Williams a comfortable start on serve.
Williams *1-2 GarciaWilliams is much more aggressive on the return this time around, playing a superb forehand to the baseline, but Garcia responds with a cross-court winner. The Frenchwoman manages to get plenty of power on her final two serves, forcing Williams to hit her returns into the net, giving Garcia another hold. It's been a composed start from Garcia, she seems to be a better match for Williams on grass than she was on the clay at Roland Garros.
Williams 2-2* GarciaGarcia mis-hits her return, catching the ball on the frame of her racquet, but the ball remains in play, deceiving Williams. However, the world number one finds a couple of big serves, including on ace, to keep her in control of the game.
Williams *3-2 GarciaBREAK! Garcia seems to have lost a little of the intensity from her serve, and Williams pounces with some impressive returns to bring up three break points. A return to the back corner of the court catches Garcia out, leaving her stretching for the ball. She manages to get her racquet to the ball, but can only hit the ball into the net.
Williams 4-2* GarciaWilliams quickly finds herself 40-0 up courtesy of some powerful and accurate serving. She seals the game with some finesse at the net, delicately volleying the ball into the open court to consolidate her break in the previous game.
Williams *4-3 GarciaWith Garcia running left to get back into the centre of the court, Williams directs her return to the right-hand side of the baseline, leaving the Frenchwoman pounding the grass with her racquet. However, she manages to channel her anger into a couple of fast serves, completing the game with an ace.
Williams 5-3* GarciaWilliams opens with an ace, before a forehand out wide causes Garcia to slip. The top seed is distracted by her opponent's fall and smashes her return long. Thankfully, Garcia seems to be uninjured. The American makes another ace, before the 19-year-old slices her return just long on the next point.
1.48pmSET! Williams 6-3 Garcia
1.49pmWilliams really attacks the Garcia serve, clearly keen to seal the first set. She brings up to set points, but the French player shows her speedy footwork to bring up deuce. A long return from Williams hands her opponent advantage, but the game heads back to deuce when she misses her volley. Some superb backhands help Williams to another set point, and she's handed the set when Garcia smashes a forehand into the net.
1.50pmWilliams' serve looked almost untouchable in that opening set. The defending champion had six aces compared to Garcia's three, while the French player made the only double fault.
Williams 6-3 1-0* GarciaWilliams is frustrated in the first point of the game as she is faced with an open court, but decides too late to come into the net to volley and ends up firing her smash long. A couple of long balls from Garcia allow the top seed to edge in front, but the American mis-judges her backhand and catches the net to bring up deuce. Two big serves are too much for Garcia to return though, and Williams escapes from a tricky service game at the start of this second set.
Williams 6-3 *1-1 GarciaGarcia drops the opening two points of the game as Williams continues her strong returning form from the first set. However, Garcia ups the pace on her serve to get herself back into the game. The world number one forces a mistake from Garcia to give herself a chance to get a break on the board, but a long return brings up deuce. Garcia saves another break point before adding some variety to her serve to force a couple of mistakes on the return from Williams, allowing her to hold serve.
Williams 6-3 2-1* GarciaGarcia makes a brilliant return at the start of the game as she seems to be adapting to Williams' serve, but the American finds another gear, quickly wrapping the game up with two aces.
Williams 6-3 *2-2 GarciaSaving break points in her previous service game seems to have given Garcia a boost as she looks super composed during a comfortable hold. She seems to be putting much more variation into her serves now, which is causing Williams difficulty when making her returns.
Williams 6-3 3-2* GarciaWilliams continues to look strong on serve, making a series of strong and accurate deliveries yet again to give herself an easy hold. Except for the first game of the second set, Garcia has not been able to test the Williams serve.
Williams 6-3 *4-2 GarciaBREAK! Williams goes for a drop shot at the start of the game, but fails to get the ball back over the net. A series of powerful forehands from the back of the court by the world number one force Garcia to over-hit the ball, bringing up break point, and Williams clinches it with a superb forehand return.
Williams 6-3 5-2* GarciaWilliams is looking so strong as she quickly takes a 40-0 lead. She is briefly rattled by a foot fault call as she gets ready to serve form the game, but quickly finds her composure, firing another big serve at Garcia, which the French player can't return. Garcia must hold next to keep herself in the match.
2.24pmA long shot from Garcia gives Williams match point.
2.25pmGAME, SET & MATCH! Williams 6-3 6-2 Garcia
2.26pmGarcia still looked calm as she served to keep the match alive. Her powerful serve forces a couple of mistakes from her opponent, before she hits a brilliant forehand winner from behind the baseline. However, Williams takes the game to deuce playing some shots from all around the court, forcing Garcia to attempt a lob which goes long. A drop shots from Garcia catches Williams out, resulting in a high-pitch squeal from the world number one, but she manages to force some more long balls from the 19-year-old, allowing the top seed to secure her spot in round three.
2.27pmGarcia showed that she was capable of providing a challenge for the world number one, but Williams was just able to up her game at the crucial moments to ensure a smooth progression into the next round, where she will play 42-year-old Kimiko Date-Krumm.
2.28pmWell that's all from this match but stick around from results and reaction to all of today's matches, as well as more live coverage from this afternoon's key matches. Thanks for joining me this afternoon.