The 27th-seeded Belarusian, whose last championship was won at Miami Gardens in 2016, required nearly three hours to defeat Putintseva 7-6 (7-4) 1-6 6-3.
A power failure interrupted the opening set for forty-five minutes.
Fourth-ranked Rybakina of the globe defeated eighth-seeded Maria Sakkari of Greece 7-5 6-7 (4-7) 6-4.
In the year-prize match of the previous year, Czech Petra Kvitova defeated Rybakina, the highest-ranked female player still in contention.
In Tuesday’s second set, Kazakhstan had two match points, but Sakkari rallied and prevailed in the tiebreaker.
After a demanding two hours and forty-eight minutes, Rybakina secured the victory with a single break of serve in the final set.
