Mirza ranked 32 in the world and seeded 21st at Indian Wells has surpassed 9th seeded Peer to reach the fourth round in this elite tournament.
Earlier, Sania Mirza got a bye in the first round and went on to beat Ukraine"s Olga Savchuk 4-6, 6-1, 6-4 in the second round. Whereas, Shahar Peer got a bye too in the first round and topped Akgul Amanmuradova 6-1, 6-4 to reach the next level.
It was Sania's fourth victory in as many matches over Peer, her former doubles partner.
"I was a bit irritated with myself, because I was fighting, fighting, the whole time, coming back all the time, levelling up and then not going up or finishing it," Sania said after the match.
Sania has also made it to the quarter-finals of the doubles event in this tournament. The 21-year-old partnering American Bethanie Mattek beat Tatiana Poutchek of Belarus and Russian Anastasia Rodionova 6-2, 4-6, 10-7 to advance to the last eight.