Down 2-0 after the opening day's action, the Czechs mounted a spirited comeback as Kvitova beat Pegula 7-6(6) 6-4 but Tomas Machac could not build on the win as he retired due to an ankle injury with Frances Tiafoe leading 6-3 2-4.
Pegula shook off the disappointment of her singles loss and teamed up with Taylor Fritz to get past Marie Bouzkova and Jiri Lehecka 2-6 6-3 10-7. The Americans, who are Group C toppers, next face Germany starting Monday.
"I feel like on our team there's a lot of different options and different pairings and the mixed could be important down the line," Fritz said. "We want to figure out what will be our best team or at least get the rust off.
"The whole thing can be decided by the mixed doubles so we want to know who we want to go with in a big match."
Greece were also comfortable victors over Bulgaria as Maria Sakkari set the tone for the 4-1 win by getting past Viktoriya Tomova 6-3 6-2 in Group A.
"I was a little nervous in the beginning," Sakkari said. "Especially being 2-0 up in the tie, I knew my match was crucial to winning. She was solid at first, but I found my game, found my serve and everything got better.
"The United Cup format is unusual but it's nice. We get to spend time together, watching each other, so we can learn a lot of things... From the outside you see things differently."
Dimitar Kuzmanov pulled one back for Bulgaria by outclassing Michail Pervolarakis 6-1 6-1 but Sakkari and Stefanos Tsitsipas carried too much power for Gergana Topalova and Adrian Andreev and prevailed 6-4 6-4.
Australia suffered a blow earlier as Ajla Tomljanovic pulled out of her match against Harriet Dart due to a left knee injury and her replacement Maddison Inglis fell 6-4 6-4 as Britain took an unassailable 3-0 lead.
Matteo Berrettini downed Thiago Monteiro 6-4 7-6(7) as Italy sealed a 3-2 Group E win over Brazil while Stan Wawrinka helped Switzerland to a 3-0 lead over Kazakhstan in Group B by beating Alexander Bublik 6-3 7-6(3).
