Congress President Rahul Gandhi termed the bypoll results as "a rejection of the BJP by the people of Rajasthan".
"Well done Rajasthan Congress! Proud of each and every one of you. This is a rejection of the BJP by the people of Rajasthan," Gandhi tweeted.
Hundreds of Congress activists burst firecrackers and danced to drum beats outside the party office here as its candidate Vivek Dhakar trounced Bharatiya Janata Party's Shakti Singh Hada by 12,976 votes. Many amongst them distributed sweets.
While Dhakar got 70,146 votes, Hada secured 57,170 in the by-election held on January 29, Election Commission officials said.
The election followed the death of BJP MLA Kirti Kumari due to swine flu in August last year.
In Ajmer, with 61 per cent of the vote count over, Raghu Sharma of the Congress was leading by 77,868 votes by securing 391,754 votes. The BJP's Ram Swaroop Lamba had got 313,706 votes.
In Alwar, after 82 per cent of the vote count done with, Karan Singh Yadav of the Congress was leading by 144,914 votes. He had garnered 520,434 votes, leaving behind Jaswant Singh Yadav of the BJP at 375,520 votes.
Congress candidates led from the beginning in vote count in both the Lok Sabha seats and edged past the BJP in Mandalgarh after initially trailing at the second spot.
A total of 42 candidates were in the fray in the three seats, all of which were held by the BJP. There were 23 contestants in Ajmer and 11 in Alwar.
The elections to the Lok Sabha constituencies were necessitated by the deaths of Sanwarlal Jat (Ajmer) and Mahant Chand Nath Yogi (Alwar).