The BJP was leading in 24 of the 25 seats where leads were available till 9.30 a.m.
However, in Barmer, expelled BJP leader Jaswant Singh, who is fighting as an Independent, was leading over his BJP rival Col. Sonaram.
Prominent BJP leaders who were leading included sitting Bikaner MP Arjun Ram Meghwal, and Dushyant Singh, son of Rajasthan Chief Minister Vasundhara Raje, from Jhalwar-Baran.
The Congress, which had 20 members in the last Lok Sabha election from Rajasthan, was recording one of its worst defeats in the state's history.
Union ministers Sachin Pilot (Ajmer), Bhanwar Jitendra Singh (Alwar), Girja Vyas (Chittorgarh) and Chandresh Kumari (Jodhpur), and party leader Raj Bala Ola (Jhunjhunu) were trailing.
"It is just the beginning... we hope to recover and perform better," said Congress leader Sushil Sharma.
"We hope to win on all the 25 seats," said state BJP vice president Onkar Singh Lakhawat.