NEW DELHI—Passenger-car sales in India grew at the fastest pace in five years in 2015, the latest sign that consumer sentiment in the world’s fastest-growing major economy is picking up.

A decline in fuel costs as global crude-oil prices slid, lower interest rates—down by about a percentage point, according to the Society of Indian Automobile Manufacturers—and auto makers’ price incentives helped drive the increase. Sales last year were up 9.8% to 2.03 million cars, accelerating from 2014’s 2.5%, according to data issued Monday by...