The 24-year-old star, ranked No.4 in the world and among the favourites for next month's Australian Open, dropped the first set but fought back to win 4-6 6-2 7-6 (7-4) in Perth.
The tough triumph came after compatriot Despina Papamichail prevailed over Isabella Shinikova in a similar manner, coming from a set and a break down to win 3-6 6-4 6-1.
The results gave Greece a perfect start to the mixed teams event, with women's world No.6 Maria Sakkari poised to enter the fray on Friday.
Sakkari will take on Viktoriya Tomova, while Michail Pervolarakis meets Dimitar Kuzmanov.
Sakkari and Tsitsipas are set to team up for Greece in the mixed doubles against Tomova and Dimitrov
Tsitsipas has been an Australian Open semi-finalist in three of the last four years and reached the French Open final in 2021, but is yet to win a major.
There is hope 2023 will be the year he makes his breakthrough at Melbourne Park, and his fighting win over the experienced Dimitrov was a positive start to the season.
Tsitsipas saved three set points on his own serve before conceding the first break, and set, of the match.
He controlled the second set and crucially saved two break points at 3-4 down in the third.
Tsitsipas revved up the crowd after holding to level the set and kept his cool in the tiebreak.
The US also won both their matches on day one, with Taylor Fritz and Madison Keys beating their Czech Republic opponents in Sydney.
World No.9 Fritz had an impressive 6-3 6-4 victory over Jiri Lehecka, while Keys accounted for Marie Bouzkova 6-4 6-3, continuing her love affair with Australia.
The 27-year-old's semi-final finish at the most recent Australian Open was her best result at a grand slam since 2018 and followed her triumph at the 2022 Adelaide International.
"I love playing here," Keys said.
"Whether it's the people or that I like playing in the heat at the start of the year, it's fast and bouncy, it suits my game really well."
The Italy-Brazil tie in Brisbane is evenly poised at 1-1 after rising star Lorenzo Musetti beat Felipe Melegeni Alves 6-3 6-4.
World No.15 Beatriz Haddad Maia had got Brazil off to a fast start with a 6-2 6-0 thrashing of Martina Trevisan before 20-year-old Musetti hit back for the Europeans.
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