Hingis and Mirza captured their third doubles title in as many tournaments, after triumphs in the Indian Wells and Miami hardcourt events.
The duo hadn't dropped a set in their two prior tournaments, but they were tested on the green clay courts of Charleston, saving a match point against Anabel Medina Garrigues and Yaroslava Shvedova in the semi-finals.
On Sunday they defeated Casey Dellacqua and Darija Jurak 6-0, 6-4 to lift the trophy.
Mirza becomes the first Indian woman to reach number one in either singles or doubles.
She has won seven WTA doubles titles over the last 12 months - Oeiras, Tokyo and the WTA Finals last year with Zimbabwe's Cara Black, Sydney this year with American Bethanie Mattek-Sands, and her three titles with Hingis.
She also won her third Grand Slam mixed doubles title last September at the US Open, with Brazilian partner Bruno Soares.