Flying from New York, you can also find similar deals on flights to Mumbai from late September into November, as first highlighted by Secret Flying.
To get a good flight, you'll want to search for flights from China Eastern Airlines or Air China on Momondo. You'll find some deals via Google Flights, but the prices are significantly lower on the former site.
One thing to note on these routes is they're not the fastest treks you're going to find. To some extent, that should be expected at these prices. One return trip for a $527 roundtrip flight to Mumbai had you spending a day in Beijing. On the upside, a trip with a long layover might just be a bonus getaway somewhere fun. If you're up for an adventure, the layover might not be a bad thing. (There are times when a layover is a feature of your adventure.)
As for other US departure cities, there are some deals if you're willing to dig, but the prices aren't quite as notable as the fares flying out of New York. Maybe try your luck on a flight to Hawaii.
h/t Secret Flying
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