VARANASI, India — Early vote counting suggests Indian Prime Minister Narendra Modi will win a rare third term on Tuesday, entering a new decade as leader of the world’s most populous country at a time when India is growing closer to the U.S. and gaining clout around the world. 

Modi enjoys wide support both at home and among the large Indian diaspora in the U.S. and elsewhere, with voters rewarding a leader they see as responsible for India’s rocketing economy and rising confidence on…