"We didn't know how to play them that well in the beginning," Hingis said in their post-match press conference. "We lost an opportunity at 3-2, 40-0 to go up and close out the match, and they came back to play a couple of really good games - especially Ostapenko, who hit some really great shots.
"I think it was great experience for them to play a match like that, and also for us to get into the tournament. I'm definitely happy we didn't have to play a deciding set. It's always nice to close out in straight sets; it makes us that much stronger."
Hingis and Mirza haven't lost a match since last August at the Western & Southern Open, their now-37-match winning streak having taken them to titles at the US Open, BNP Paribas WTA Finals Singapore presented by SC Global, and the Australian Open - with only the French Open standing between them and a possible "Santina Slam."
"The streak that we're on is amazing," Mirza said. "To be honest, we knew we could play good, but not this good. We're surprising ourselves as well, and we just want to keep going.
Asked about the media's fascination with their streak, the longest since Jana Novotna and Helena Sukova won 44 straight matches in 1990, the team known as "SanTina" didn't mince words.
"We're counting, also."
"Yes, we are," Hingis added.
For Hingis, the partnership with Mirza marks her second to truly capture the imagination of the tennis world, the first being her late-90s domination with Russia's own Anna Kournikova - still a popular topic in the St. Petersburg press room.
"She was a great player, a team player, and we had great times for those two years," Hingis said, speaking about their two Australian Open victories in 1999 and 2002.
"She kind of was the one who started this Russian Armada - or Russian generation - along with Elena Likhovtseva. She was definitely the one who you could aim for and be like, go around the world and live the 'Russian-American dream.' I loved playing with her.
"We stay in touch, especially during the Miami event; we always try to see each other. I follow what she's doing; she follows me."
Mirza too fondly remembers the "Spice Girls" of the women's doubles circuit.
"At that time I think TV was not as evolved as it is today, combined with the computer, so it was not so easy to get to see matches all the time. But everybody knew Martina Hingis, everybody knew Anna Kournikova, and everybody knew that this partnership was winning a lot, and probably was one of the best doubles teams to play.
"She's not that much older than me," she added with a laugh. "Only five years; it's just that she's been around for such a long time!"
Another partnership Hingis looks forward to exploring involves fellow Swiss Roger Federer, who agreed to play mixed doubles with her at the upcoming Olympic Games in Rio de Janeiro.
"I waited ten months, and maybe after winning a lot with Sania, and becoming No.1 again and winning three mixed titles, I was hoping that would be persuasion enough to partner up."
SanTina next face an all-Russian pair for a spot in the quarterfinals and Win No.38: rising Russian star Daria Kasatkina and Elena Vesnina, Mirza's former doubles partner.
"We played together for a long time; she's a very good friend of mine, and we've known each other since we were 13 years old.
"I have a feeling that the crowd will be behind them because she's quite popular here, but hopefully there will be some people supporting us."
Asked if they foresaw their partnership transcending to other endeavors, Hingis said they planned to let their racquets do the talking.
"We'll stick to tennis; that's what we do best."