In a hard-hitting battle it was Williams who had the clear upper hand early on, storming out to a 4-1 lead and eventually closing the first set out, 6-3. A loose Williams service game in the eighth game of the second set gave Hlavackova a 5-3 lead, but Williams clawed back and made one huge push at the end to finish it off - she won 11 of the last 12 points of the match to clinch the victory, 63 76(1).
"I'd never played her in singles but I've played her many times in doubles. I knew how determined she is and that I had to play really well," Williams said. "The first match you don't always know exactly what's going to happen and that you just have to fight and try hard, and that's really what I did today.
"It was a great first match, and I'm looking forward to putting better points together with every game."
Williams was asked afterwards about taking her game to another level in the second set tie-break.
"When I got to the tie-breaker I was like, 'I'm gonna go for it.' That's kind of how I was playing that tie-breaker. I just wanted to take control. I think it was the most control I had the whole match. The rest of the match she was really trying to control the points, so I had to change the dynamic there."
Next up for Williams is Yvonne Meusburger, who pulled off the first upset of the tournament by beating No.7 seed Mona Barthel, 64 63. The two veterans will be playing against each other for the first time.
"She won her first title last year - I watched it on the Tennis Channel and I was really happy for her!" Williams said. "I won't be as happy for her in our match. I'll try to be happy for me to get the win."
"It was the first match of the season, Tamira and I are both coming off injuries and the conditions were windy - so overall it was really tough conditions for both of us out there," Hampton said. "I'm happy that I pulled through in the end and got the W today, but I'm hoping to improve for the next round.
"The first set was probably one of the worst sets of tennis I've played in a while. But I was really nervous. I hadn't played a match since the US Open, so nerves, conditions, all of it put together."