Wild card Williams won 7-5 6-2 on centre court as she maintained her streak of never having lost a set to Davis, having beaten her four times.
Williams fended off seven of the eight break points she faced, and won 61% of points when returning the Davis second serve.
"I was just trying to find the rhythm," Williams said afterwards. "She has a surprisingly powerful game. You look at her and you don't think she's gonna hit that hard, but she really knows how to control the point - has an impressive game."
Kazakhstan's Yulia Putintseva and Belarusian Aliaksandra Sasnovich earlier won three-set matches.
Putintseva defeated Jelena Ostapenko of Latvia 6-2 7-6(3) 6-3 and Sasnovich beat Astra Sharma of Australia 6-1 4-6 6-1.
Aryna Sabalenka had an easier task, beating Petra Martic 6-1 6-4.