The party had won 96 seats in 2008.
Poll result trends showed Sunday that the Congress is likely to finish with 27 to 30 seats out of the 199 seats for which polling was held.
In Churu constituency, polling has been postponed to Dec 13 because of the death of the Bahujan Samaj Party candidate last month.
Poll result trends showed Congress is likely to finish with 27-30 seats
Before the polls this year, the Congress' lowest tally was in 1977 when it won 41 seats.
Prominent Congress leaders who lost or are trailing include big names like Shanti Kumar Dhariwal, urban development minister in the Ashok Gehlot government, A.A. Khan, medical and health minister, Virendra Beniwal, transport minister, Bina Kak, tourism minister, Deependra Singh Shekhawat, assembly speaker and Rajendra Pareek, industries minister. PWD Minister Bharat Singh and Revenue Minister Hemaram Chaudhary are also trailing.
Winning or leading candidates from the Congress were few and included Chief Minister Ashok Gehlot from Sardarpura constituency in Jodhpur, Mahendrajeet Singh Malviya and Pradyuman Singh.
"No one expected this kind of result really, not even the BJP was expecting this," said Ravi Goswami, a political analyst.
"It seems "double anti-incumbency", (with Congress being in power both in the state and at the centre) and the Narendra Modi wave have contributed to the defeat of the Congress in the state," Goswami said, adding that a detailed analysis can be done only after the final results are in.