The No.1-seeded Williams beat Tatishvili in just 51 minutes, firing 27 winners to 14 unforced errors. Meanwhile, she didn't let any winners past her in the first set, and only four in the second set.
The numbers keep piling up for Williams - not only did she extend the aforementioned career-best winning streak to 25 matches, she has now won 85 of her last 89 matches, a stretch that dates back to the beginning of last year's clay court season. She is also 50-1 in Grand Slam first round matches.
It was a stark contrast to her dramatic loss to Virginie Razzano in the same round a year ago.
"I was nervous - I'm always a little nervous going into first round matches at Slams," Williams said. "This time I wasn't as nervous as I was at other Grand Slams, though. But for the most part I felt pretty safe and felt good about my game and that if I just do what I did in practice, I'll be okay."
Williams is trying to win the French Open for the second time, her first time coming back in 2002 - her success at the other Grand Slams is far bigger, having won each of them four or more times.
"I just keep trying here, and it hasn't been working out for me," Williams said. "I just think I may have gotten nervous in the past or may have basically choked a few matches away, and played some opponents that played well, but I have probably had opportunities and given them away. Some matches I just lost because I wasn't intense enough or I didn't do enough work before I got here."
Next for Williams is a wildcard, both literally and figuratively - Caroline Garcia, a French teenager with a lot of promise, blasted 19 winners to make it past Ukrainian qualifier Yuliya Beygelzimer, 63 64.
Garcia made a huge impression on the tennis world on Chatrier two years ago, building a 63 41 lead against Maria Sharapova, putting on a dazzling display of aggressive all-court tennis along the way. She would lose that match in three sets, but everyone took notice, including ATP World Tour star Andy Murray, who said on Twitter she would be 'No.1 in the world one day' - Martina Navratilova agreed.
Sharapova beat Garcia in straight sets earlier this year in Doha and continued to pile on the praise. "I think we will be seeing her for many more years," the Russian said. "She has a big game and many strengths, which I think everyone saw out there today. I think she has a bright future ahead of her."
Garcia was asked about the match with Sharapova after her first round win over Beygelzimer.
"That was two years ago - I've grown up since then," Garcia said. "Serena is No.1, she has won four titles in a row, she has so much experience. She knows how to manage at the Grand Slams. She will be the really big favorite, but I've got to play my game and just believe in my game until the end."
Williams and Garcia will be playing against each other for the first time.