BJP's likely victory after 15 years of Congress rule was tempered by an unexpectedly strong showing by the new anti-corruption Aam Aadmi (Common Man) Party, which could deny it the majority required to rule.
Supporters of the new party celebrated in the streets, waving brooms to symbolise sweeping out rotten politicians after several years of spectacular corruption scandals.
"The Aam Aadmi Party has brought idealism into politics," said AAP activist Atishi Marlena.
Final results were expected by early afternoon for the elections in Delhi, Chhattisgarh, Madhya Pradesh and Rajasthan.
BJP-ruled Chhattisgarh was the tightest race and the one possible bright spot for Congress, which had a slight lead in early counting. Congress has benefited from voter sympathy after much of its state leadership was wiped out in an attack by Maoist militants there earlier this year.
A small north-eastern state, Mizoram, is due to report results from its election on Monday. Exit polls forecast Congress lost ground there, as well, to local ethnic parties.