Running in the third leg, Ashwini, who earlier clinched the yellow metal in the 400m hurdles, gave the Indian team a huge lead over second-placed Kazakhstan for Mandeep Kaur to maintain it till the finishing line in 3min 29.02sec.
In the first leg, India's Manjeet Kaur was running second before Sini Jose gave a slender lead for Ashwini to take over.
Kazakhstan took the silver in 3:30.03 while China claimed the bronze in 3:30.89.
With the gold medal here, the Indian quartet have won their second gold in two months in a multi-sporting event, having won the title in the Commonwealth Games in New Delhi, though today's effort was well below 3:27.77 in the CWG