The No.1-seeded Williams dropped serve once early on but for the most part was just too strong on her delivery, holding her other nine service games and unleashing 11 aces en route to a 64 64 victory.
"It was an intense match, which was really good," Williams said. "She's a good player. She's been in the Top 10 before and she was on her way to being even better. So it was a really good match for me.
"I usually have a lot of nerves, but when I realized who I was playing I felt like it was a really good opportunity for me to have a tough match early on. That kind of made me more calm than anything."
Williams has beaten Cibulkova in all three of their previous meetings, but barely won their only previous hardcourt meeting - Cibulkova led 62 41 before Williams came roaring back to prevail, 26 64 62.
"She's such a tough player. She's fighting for every point. She had like a super long match today," Williams said of the Slovak. "I went out and I practiced and they were already playing. I came back, sat down, ate, played a game on my iPad, and I looked up and they were still on the court. I got my ankles taped and then she was just walking off the court. So that just goes to show you the fight she has.
"We've had a lot of tough matches, so I have to just go out there and stay relaxed and have one."
That match will be on Thursday, giving Williams a day off - will she celebrate New Year's Eve?
"I don't celebrate New Year's Eve, so usually I'm in bed at midnight," Williams commented. "I always hear the fireworks though. They wake me up at midnight. Hopefully I can sleep through them tonight.
"I'm a very serious player. I never leave my room during a tournament, so I'm not going out."