Sakkari's 6-3 6-2 victory on Friday gave Greece an unassailable 3-0 lead in the tie after world No.4 Stefanos Tsitsipas and Despina Papamichail posted tough three-set singles wins a day earlier.
Tomova went blow for blow with Sakkari early at RAC Arena.
But when Tomova tweaked her left calf with the scores locked at 3-3, the match turned on its head.
Sakkari held serve and then broke straight after the world No.90 took an injury break on the way to winning the first set in 52 minutes.
With Tomova's mobility compromised, Sakkari merely moved her opponent around the court as much as possible in the second set to seal the win in 87 minutes.
Sakkari committed 22 unforced errors in the first set, but she made just four in the second in a much cleaner display.
Her 19 winners for the match dwarfed that of her opponent (10).
"We're very happy to get three wins," Sakkari said on court after the match.
"I'm very grateful that I actually have a great team behind me.
"They're amazing people. We get along really well. We love coming here with the large Greek community. We want to make it to the end (the final)."
Sakkari made the semi-finals at the French Open and US Open in 2021, and this year she reached the semi-finals of the season-ending WTA Finals.
The 27-year-old is eager to break through for a maiden grand slam triumph in 2023, and she's taken her fitness to a new level during the off-season in a bid to achieve her goal.
"He (my trainer) pushed me really hard and it's something I really like to do," Sakkari said.
"Going to the gym is like my hobby.
"If I'm not fit on the court, I feel like I can't play my best tennis.
"When I feel like I can move well and I can hit powerful shots, then I feel like I'm a very good and dangerous player."
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