The sixth seeded Indo-Russian pair staved off very strong resistance from the Americans for a 6-3, 5-7, 7-6 (6) win in the marathon quarter-final, which lasted three hours and five minutes.
This is only the second time in Sania's career that she has reached a Grand Slam semi-final in the women's doubles event.
In 2011, she had reached the Wimbledon semis with Elena, losing to Kveta Peschke and Katarina Srebotnik.
Sania and Elena will now fight it out with the Russian combo of Svetlana Kuznetsova and Vera Zvonareva for a place in the summit clash.
The other semifinal will be played between the 11th seeded Italian pair of Sara Errani and Roberta Vinci and seventh seeded Czech combination of Andrea Hlavackova and Lucie Hradecka.
The deciding third set lasted 93 minutes, which was more than the duration of the first two sets.
Sania and Elena saved eight breakpoints in the third set, apart from converting two and dropping their serve twice in the final set.
In the match tie-break, the two pairs were going neck and neck but Sania and Elena held their nerves and clinched the issue.
Meanwhile, in the junior competition, Rutuja Bhonsle and Indonesia's Aldila Sutjiadi came from behind to reach quarter-finals of the girls doubles quarter-finals.
They beat the Australian pair of Naiktha Bains and Danielle Wagland 5-7 6-2 10-5 in the second round clash.
They face Irina Maria Bara of Romania and Latavia's Jelena Ostapenko, who got a second-round walkover from second seeds Dutch Indy De Vroome and Estonia's Anett Kontaveit.