AAP supporters waving the party symbol, the 'jhadu' (broom).
When counting is completed, the BJP may find itself an excruciating few inches short of the finish line.
Leads at noon showed the party ahead in 34 seats - one short of the half-way mark in the Delhi Assembly.
The incumbent Congress was comprehensively crushed -it's likely to manage just nine seats. Its 75-year-old leader, Sheila Dikshit, has sent her resignation letter to Lieutenant Governor Najeeb Jung.
"We concede defeat, we need to analyse what went wrong," said Ms Dikshit, who was not only rebuffed by voters in her quest for a record fourth term but also lost in her own constituency New Delhi to Arvind Kejriwal, who is incontrovertibly today's show-stopper in Delhi.
The former tax inspector's one-year-old Aam Aadmi Party, won 27 seats, a whopping electoral premiere. Its leaders have dismissed the possibility of supporting either the Congress or the BJP, if Delhi is mired in a hung assembly.
"Our party doesn't worry about things like who will be chief minister. We worry about how to help the country," Mr Kejriwal had said this morning.
BJP spokesperson Nirmala Sitharaman said the AAP, as "the new kid on the block" has proven it's a force to reckon with. But she said the AAP may find it tough to sustain its current popularity all the way to the national election.
"We are not interested in breaking the AAP, or trying to take some of its candidates," she said on NDTV. Earlier today, AAP leaders said some of their candidates are being approached by the BJP to switch teams.