Christina McHale and CoCo Vandeweghe, who were wildcards into the draw, broke the Hingis serve for a 2-1 lead in the first set, but from there it was all Hingis and Mirza - the No.1-seeded Swiss-Indian duo powered through 11 of the next 14 games to move through in an hour and three minutes, 6-4, 6-1.
"Unlike the guys, in women's tennis a lot of the singles players play doubles, and they beat some good teams to get here," Mirza said. "It's almost more dangerous to play teams like that because they really have nothing to lose, and we also don't really know how to play them because they're a new team.
"They're both talented, they're both young, and they have a great future ahead of them. If they keep playing together I'm sure we'll be seeing them in the later rounds of tournaments in the future."
Mirza also said their first match of the week, a tougher 7-6(3), 6-4 victory against Julia Goerges and Klaudia Jans-Ignacik on Wednesday, helped them out in their quarterfinal against the Americans.
"Our first match was really tough. We weren't playing our best tennis. But we dug through it, and sometimes when you win matches when you aren't playing well, you feel more confident in the next one. So today we came out feeling a lot better, for sure. Today we were almost back to our best.
"We could do better, but we're happy to be back in the semifinals again like last week."
After an early finish - they were off the court at 12:16pm - what will they do the rest of the day?
"Maybe go to the shops a little bit!" Mirza said. "We have a joke going on, that after every win here we're going to go and buy something. So we might go to the mall again today - we have all day!"
Awaiting Hingis and Mirza in the semifinals will be Chan sisters Hao-Ching and Yung-Jan, who won an absolute marathon later in the day against Sara Errani and Flavia Pennetta, 6-7(4), 7-6(1), 19-17.