Nadal has only played four matches this year, two for Spain in the inaugural United Cup and two at the Australian Open, where he lost in the second round to Mackenzie McDonald.
Her opening 7-6(6), 6-4 triumph over World No 3 Jessica Pegula was a huge confidence boost for the former World No 2, who saved seven set points in the first set to win in two.
Team Greece's star player Tsitsipas, though, persevered to secure victory at RAC Arena, defeating his opponent 4-6, 6-2, 7-6(4) to give his country a 2-0 lead in the Group A match.
The historic-high prize pool is a result of a record AUD 76.5 million for the Australian Open 2023 (a 3.4 per cent increase) as well as the addition of the lucrative new United Cup event.
The inaugural United Cup brings together the best ATP Tour and Hologic WTA Tour players in an 18-country teams' event played over 11 days across three Australian cities - Brisbane, Perth and Sydney.