Hingis, 34, and 28-year-old India star Mirza came from a set down and 2-5 behind in the final set to beat Russian duo Ekaterina Makarova and Elena Vesnina 5-7, 7-6 (7/4), 7-5.
It was the top seeds' first Grand Slam title as a team having only decided to play together in March this year.
Hingis won the Wimbledon doubles with Helena Sukova in 1996 and Jana Novotna in 1998.
For Mirza, it was a maiden women's doubles title at a Grand Slam although she has won three mixed doubles titles at the majors.
Hingis can be back amongst the silverware on Sunday when she and Leander Paes face Alexander Peya and Timea Babos in the mixed doubles final.