Mirza and Croatia's Ivan Dodig, who are seeded fourth, needed an hour and 18 minutes to see off the Japanese duo of Yusuke Watanuki and Makoto Ninomiya 7-6 (5), 6-2 to enter the mixed doubles third round.
The Indo-Croatian duo finished its second round match with six aces and four double faults.
They next face the defending champions Henri Kontinen and Heather Watson for a spot in the quarterfinals.
Mirza and Flipkens scripted a 6-3, 3-6, 6-4 victory in one hour and 45 minutes.
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The 13th seeded pair will next take on third seeds Martina Hingis of Switzerland and Yung-Jan Chan of Chinese Taipei for a place in the quarterfinals.
Partnering Japan's Eri Hozumi, Raja carved out a win in his first round mixed doubles match over the American-Czech pair of James Cerretani and Renata Voracava 5-7, 6-4, 6-2.
A month after winning the French Open, Rohan Bopanna and Gabriela Dabrowski continued their winning run in mixed doubles.
The 10th seeded Indo-Canadian duo eked out a 7-6(2), 7-5 victory over the French-Romanian combine of Fabrice Martin and Raluca Olaru for a place in the third round.