In recent weeks, an army of AAP volunteers has trudged through the alleys of the city's poorest neighborhoods to try to tap a deep vein of dissatisfaction that has gripped New Delhi residents, particularly over corruption and a soaring cost of living.
The BJP's campaign highlighted runaway inflation, increasing crimes against women and shortages of power and water in the city of nearly 17 million people.
"It is time for the Congress to quit," said Harsh Vardhan, the BJP's candidate for the chief minister's post.
He appeared to voice some concern of a possible spoiler role for the AAP, saying a vote for Kejriwal would be "a wasted vote."
Dikshit stressed her party's development agenda over the past 15 years, citing the city's popular subway system, numerous overpasses and environmental efforts among the achievements of her tenure.
Early Wednesday, Dikshit and Sonia Gandhi, the chief of India's ruling Congress party, voted at a polling station in central New Delhi. They then showed their inked fingers to television cameras before appealing to citizens to come out and vote.
Their appeal appeared to work in the poorer neighborhoods of the capital, where people crowded polling stations. In contrast, the turnout was low in the more affluent pockets of the city.
While Dikshit was confident her party would win again, analysts said the 76-year-old Congress veteran's chances could be stymied by her party's ebbing support.
In recent months, Prime Minister Manmohan Singh's government has been hit by a slew of corruption scandals, adding to public anger over its failure to push through much-needed economic reforms to revive a slowing economy.
The BJP appeared ready to cash in on the Congress party's woes.
"We are very confident," the BJP's candidate, Harsh Vardhan, said Wednesday. "It's going to be a hands-down victory for the BJP."
Kejriwal urged people to vote in large numbers. "It's the people's election," he told reporters after he voted. "We have put everything we have at stake. Now it is up to the people to decide."
Vote counting in Delhi and four states that also held elections this month is scheduled for Sunday, with the results expected to be announced that evening.