While balloting was initially slow in middle and upper middle class areas, polling centres in low income neighbourhoods witnessed virtual mobs right from the time the exercise began at 8 a.m.
Among the early voters were former chief minister and Aam Aadmi Party leader Arvind Kejriwal, who was greeted by crowds of supporters, and Bharatiya Janata Party's chief ministerial candidate Kiran Bedi besides Congress leader Ajay Maken and Congress president Sonia Gandhi.
Midway through the balloting that ends at 6 p.m., both the AAP and the BJP claimed they were poised to win.
Home Minister Rajnath Singh said in Lucknow that the BJP would get a clear majority in the 70-member Delhi assembly.
After voting in a government school in south Delhi, Bedi flashed a V sign and asked people to vote for a "clean, literate and safe Delhi".
"Today is a historic day for Delhiites. It's the day for them to decide what type of Delhi they want," said the country's first woman police officer, picked by Modi to lead the BJP charge in the capital.
Journalist-turned-AAP leader Ashutosh told IANS: "We are confident of winning and forming a government in Delhi. According to our estimates, we will win 40-42 (of the 70) seats."
Prime Minister Narendra Modi urged voters to exercise their franchise in large numbers. "I particularly call upon my young friends to vote in record numbers."
Kejriwal too asked people to vote in large numbers -- and resists attempts by political parties to woo them with bribes.
While the mood was relaxed at polling stations, political parties lodged complaints against one another.
The AAP urged the Election Commission to act against Bedi, saying she took part in a 'padyatra' and a bike rally in her Krishna Nagar constituency.Bedi accused the AAP of wooing voters with bribe. Kejriwal denied this and said the BJP was spreading rumours.
Although the Congress, which ruled Delhi for 15 years until December 2013, is also in the race, most pundits say Delhi's battle for power is mainly between the BJP and the AAP.
Sonia Gandhi was mellowed when asked about her party's prospects. "Jo janta chahegi wahi hoga (What people want will happen)", she said after casting her vote.
The highest voting till 3 p.m. was reported from Seelampur (58.52 percent) and Mongolpuri (57.78 percent), both low income areas.
The elections are taking place a year after Kejriwal resigned after being the chief minister for 49 tumultuous days.
There are 673 candidates in the fray now. Voting took place in 11,763 centres."I have cast my vote," said Ravi Kumar, a resident of Malviya Nagar in south Delhi, showing off his left forefinger with the purple indelible ink stain on it as proof.
Added east Delhi resident Rajendra Sharma: "It is our duty to vote."
Vice President Hamid Ansari also voted. But President Pranab Mukherjee did not although he went to the polling booth. He had not voted in the 2014 Lok Sabha election too, saying the president is above party politics.
Supporters of political parties were huddled near polling booths.
A government official on election duty in east Delhi hoped that elections would throw up a clear mandate.
"I do not want another fractured mandate and another election. It is a lot of work for us," he said.
The election result will come out Tuesday.