Prime minister Narendra Modi’s Hindu nationalist party is seeking reelection for another five years.
The voting on Sunday also covers Mr Modi’s constituency of Varanasi, a holy Hindu city where he was elected in 2014.
He spent Saturday night at Kedarnath, a temple of Hindu god Shiva nestled in the Himalayas in northern India.
The last round of the elections includes 59 constituencies in eight states.
Up for grabs are 13 seats in Punjab and an equal number in Uttar Pradesh, eight each in Bihar and Madhya Pradesh, nine in West Bengal, four in Himachal Pradesh and three in Jharkhand and Chandigarh.
Counting of votes is scheduled for May 23.
In Kolkata, the capital of West Bengal, voters lined up outside polling stations since early morning to avoid scorching heat with temperatures reaching up to 38C (100.4F).
Armed security officials stood guard in and outside the centres amid fear of violence.
Mr Modi is challenged here by Chief Minister Mamata Banerjee, who heads the more inclusive Trinamool Congress party and eyes a chance to go to New Delhi as the opposition’s candidate for prime minister.
Mr Modi has visited West Bengal 17 times in an effort to make inroads with his Hindu nationalist agenda that had provoked sporadic violence and prompted the Election Commission to cut off campaigning.
The election is seen as a referendum on Mr Modi’s five-year rule. He played up the threat of Pakistan, India’s Muslim-majority neighbour and arch-rival, especially after the suicide bombing of a paramilitary convoy on February 14 that killed 40 Indian soldiers.
Mr Modi’s Bharatiya Janata Party (BHP) main opposition is the Congress party, led by Rahul Gandhi, the scion of the Nehru-Gandhi dynasty that has produced three prime ministers.
Congress and other opposition parties have challenged Mr Modi over a high unemployment rate of 6.1% and farmers’ distress aggravated by low crop prices.
Some of Mr Modi’s boldest policy steps, such as the demonetisation of high currency notes to curb black-market money and bring a large number of people into tax net, proved to be economically damaging.
A haphazard implementation of “one nation, one tax” — goods and services tax —also hit small and medium businesses.
Voter turnout in the first six rounds was approximately 66%, the Election Commission said, up slightly from 58% in the last national vote in 2014.
Pre-election poll surveys by the media indicate that no party is likely to win anything close to a majority in Parliament with 543 seats.
The BJP, which won a majority of 282 seats in 2014, may need some regional parties as allies to stay in power.
A Congress-led government will require a major electoral upset.