The Congress president took to Twitter to congratulate his partymen, saying that he was proud of each one of them.
"Well done Rajasthan Congress! Proud of each and every one of you. This is a rejection of the BJP by the people of Rajasthan. #RajasthanByPolls," he tweeted.
Congress leaders P Chidambaram and Randeep Surjewala also congratulated the party leaders and people of the desert state for the stupendous victory of Congress.
At the Congress headquarters here, party workers danced to the beating of drums.
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The Congress thumped the ruling BJP in Rajasthan, clinching all the two Lok Sabha and one state Assembly seats in bypolls in the key cow belt state where the saffron party is eyeing a second straight term when Assembly elections are held around December this year.
Karan Singh Yadav of the Congress trounced his nearest BJP rival Jaswant Yadav by a whopping 1,96,496 votes in Alwar, while the main opposition party's nominee for Ajmer Raghu Sharma beat BJP's Swaroop Lamba by an impressive margin of over 84,414 votes, the state election office said.
The Congress's Vivek Dhakad won the Mandalgarh Assembly seat, defeating his nearest BJP rival Shakti Singh Hada by nearly 13,000 votes.