Candidates of the PDP led by Mufti Mohammed Saeed surged ahead in 13 of the 25 seats where early trends were available, officials said. The state assembly has 87 seats.
The BJP was ahead in seven seats, the Congress and the ruling National Conference in two each and an independent in one seat.
Most exit polls have predicted a hung assembly in Jammu and Kashmir, the country's only Muslim-majority state.
Minister of State in the Prime Minister's Office Jitendra Singh told CNN-IBN that the BJP was "going to make history in Jammu and Kashmir".
A total of 48.29 lakh votes are to be counted.