NEW DELHI—India’s economic expansion accelerated last quarter as robust growth in manufacturing helped it pull further ahead of China as the world’s fastest-growing big economy.

Gross domestic product in the three months ended Sept. 30 grew 7.4% from a year earlier, according to government data released on Monday. That was a step up from the 7.0% expansion in the previous quarter and in line with the 7.4% median forecast of economists polled by The Wall Street Journal.

As...