Alcaraz has beaten Zverev twice in a row, but the German has been the better player in faster conditions.
Viktoria Hruncakova and Tereza Mihalikova completed the surprise victory, surviving a late rally by Taylor Townsend and Ashlyn Krueger.
As Williamson returns, one of the star performers in the historic series win over India, spinner Ajaz Patel, has been dropped.
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