The world number one faced four break points in the opening game of the match, but was never tested again as she cruised past her compatriot.
The top seed will face either Christina McHale or Chanelle Scheeper in the second round.
Read how all the action unfolded below:
5.37pmGood evening! World number one Serena Williams will be getting her Wimbledon campaign underway shortly against Anna Tatishvili, who is currently 113th in the WTA rankings. The players should be making their way out to Centre Court in the next couple of minutes.
5.39pmThis will be just the second time that these two players have met. Their only previously match was last year on clay at Bastad, with Williams cruising past the 24-year-old 6-2 6-3.
5.41pmThis will be an interesting tournament for Williams. She comes into the event as the heavy favourite, but it was the same last year when she was knocked out in round four by Sabine Lisicki, while she is also fresh from a second-round exit at the French Open, where she had been the defending champion.
5.42pmHere are the players! There's a big cheer for the top seed, although there are still a few empty seats as spectators take a break following Rafael Nadal's match which has only recently finished. As ever, the two players will be given a few minutes to warm up and get used to the conditions on the court before the match gets underway.
5.45pmOn paper, this should be a pretty comfortable match for Williams. Tatishvili, who only started representing America in April, is outside the top 100, although she has a career-high ranking of 50, and has never been past the second round at Wimbledon. In fact, her last win in a Grand Slam came in 2012 when she reached the fourth round of the US Open.
5.48pmRight then, the players are ready to go, with Williams serving first.
5.57pmThere could be trouble for the top seed in a lengthy opening game. Williams has already had to save four break points against her opponent, with the game returning to deuce for a seventh time.
Williams 1-0* TatishviliWell it's not the start she would have hoped for but the world number one eventually manages to hold. Williams misses a couple of serves as she find her rhythm, but blasts an ace past her opponent to take a 40-30 lead. Tatishvili defends well from the back of the court though and brings up deuce, before winning a break point with her forehand. Williams misses her first serve again but her opponent mis-hits the return off her second to let her off. The top save three more break points as Tatishvili looks to capitalise on her shaky start. It looked like Williams had settled as she brought up advantage for the first time with an ace, but a double fault on the next point sent the game back to deuce. However, she manages to dip deep to see it out with an ace, and she shouts like she's just won the tournament. That is surely a tougher start than Williams had expected.
Williams *2-0 TatishviliBREAK! Tatishvili lets Williams edge ahead as she makes a double fault, but she quickly regains her composure. However, a low groundstroke fails to clear the net to send the game to deuce before another double fault gives Williams a chance to break. While sprinting to reach a cross-court forehand from Tatishvili, the top seed loses her footing, allowing her opponent to save the break, but she quickly creates another chance, and she takes it when Tatishvili slices the ball into the net again.
Williams 3-0* TatishviliWilliams is still struggling the get her first serve in but she looks a lot more comfortable in this game than she did in the opener as she dictates the play from the baseline. Tatishvili tries to move into the court to hurry her opponent, and initially has some success as she forces a long forehand from Williams, but the world number one responds with an ace on the next point to wrap up the game.
Williams *3-1 TatishviliTatishvili serves well to open up a 40-0 lead. Another big serve as she looks to seal the game forces a weak return from Williams, and the 24-year-old is able to get on the board with a punchy forehand winner.
Williams 4-1* TatishviliA double fault from Williams gives Tatishvili a chance, but the five-time champion takes the lead with a superb forehand down the line. Tatishvili keeps herself in the game with another good return, but she can't repeat the shot on the next point as Williams wraps up the game. The world number one hasn't looked completely settled yet, but she's doing just enough to stop Tatishvili getting back into the set.
Williams *5-1 TatishviliBREAK! A double fault and a superb backhand return help Williams bring up three break points, which she converts at the first time of asking with another powerful return. She'll be serving for the set next.
6.21pmWell it's a devastating display from Serena Williams as she wraps up the opening set in just half an hour, firing three aces past Anna Tatishvili in the seventh game. In truth, Tatishvili didn't do a lot wrong in the opener, but she didn't make the most of her chances in the first game, and has been a bit inconsistent on serve. She obviously has the ability to test the world number one though.
Williams 6-1 *0-1 TatishviliWilliams tries to test her opponent early on, but Tatishvili serves well as she opens up a 40-15 lead, playing some good forehands from the baseline. Williams tries to pull it back, but her foot sticks as she tries to slide, allowing her opponent to clinch the game.
Williams 6-1 1-1* TatishviliTatishvili looks to attack, but Williams comes into the net for an overhead smash before sealing a relatively straightforward service game with an ace.
Williams 6-1 *1-2 TatishviliWilliams is currently at the end of the court partially in sunlight, while Tatishvili is completely in the shade, and the bright light appears to be hampering Williams a little as she sends a couple of forehands uncharacteristically wide, before a stroke from the baseline goes just long to hand the world number 113 the game.
Williams 6-1 2-2* TatishviliWilliams's serve is looking much stronger in this second set as she notches up two more aces, and benefits from Tatishvili's misfortune when the 24-year-old slips behind the baseline, allowing the top seed to hold to love.
Williams 6-1 *3-2 TatishviliBREAK! At 30-30, Tatishvili fires a low forehand into the net to give Williams a chance to break, but she saves it as she wrong-foots her opponent to send the game to deuce. However, Williams forces her into another mistake to give herself another break point, which she takes this time with a volley.
Williams 6-1 4-2* TatishviliIt appears to be just a formality for Williams now as she picks up two more aces as she rattles through another comfortable hold.
Williams 6-1 *5-2 TatishviliWilliams starts in clinical form, returning well to give herself two more break points, but Tatishvili digs deep to bring the game back to deuce. However, the top seed gives herself another chance as she fires the ball cross court before a forehand from Tatishvili goes long to give the world number one the game, and she'll serve for the match next.
6.49pmYet another ace brings up three match points for Williams.
6.50pmGAME, SET & MATCH! Serena Williams 6-1 6-2 Anna Tatishvili
6.51pmAfter what threatened to be a tricky tie in the opening game, Serena Williams cruises into the second round with a comfortable win over compatriot Anna Tatishvili, taking just over an hour to dispatch the world number 113.
6.52pmNext up for Williams will either be another American in the form of Christina McHale or Chanelle Scheeper of South Africa.
6.53pmWell that's all from this match, but stick around to read reports from all of the matches involving the top seeds as well as reaction. Thanks for joining me this evening, goodbye.