Nitish Kumar's Janata Dal United last year ditched Lalu Yadav and Congress and reunited with the BJP.
The bypolls in the Araria parliamentary seat and the Jehanabad and Bhabua assembly seats were the first since Nitish Kumar swapped partners.
RJD has retained Araria and Jehanabad and the BJP has retained Bhabua.
The status quo signals a triumph for Tejashwi Yadav, 28.
"This is no ordinary victory. Those who were saying that 'Laluji ab khatam ho gaye' have been given a reply. Laluji is an ideology. That ideology has won today," he told reporters.
The bypolls were seen as a test of Tejashwi's leadership skills in the absence of father and party chief Lalu Yadav, who is in jail for corruption and did not lead a poll campaign of the party for the first time in two decades.
"The people want the mahagatbandhan (grand alliance) at the national level...political parties should set aside their egos to fight a larger battle," he said on his party's performance.
In Jehanabad, the RJD's Krishna Mohan - he is the son of lawmaker Mundrika Singh Yadav whose death left the seat vacant - defeated the Janata Dal United's Abhiram Singh by a huge margin. The victory indicates that upper caste groups like Bhumihars and Brahmins have moved from the JDU towards the RJD.
Winning over Hindustani Awam Morcha (Secular) leader Jiten Ram Manjhi proved to be a big plus for Tejashwi. Jiten Ram Manjhi had quit the JDU when his son was not given a ticket to contest Jehanabad. Earlier this month, he joined the RJD-Congress alliance.

Last year, Tejashwi Yadav's refusal to quit as deputy chief minister following corruption charges became the trigger for Nitish Kumar's switch to the BJP-led NDA.
About a year ago, Tejashwi was cast in the unenviable role of saboteur. His refusal to quit as deputy Chief Minister following corruption charges became the trigger for Nitish Kumar's switch to the BJP-led NDA.
Suddenly pushed to the role of the opposition leader in the Bihar assembly, Tejashwi sharpened his political skills while keeping up his frequent attacks on Nitish Kumar. What he lacked in wit - his father is unmatched - he made up for in aggression.
Over the past few months, Tejashwi has shown his most combative face to Nitish Kumar, the man he once called "Chacha".
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In rallies, he deftly used his father's conviction in the fodder scam to try and win people's sympathy. He also accused the JDU and BJP of targeting him using investigative agencies.The cricketer-turned-politician was mostly mocked by the JDU and BJP as a "bachcha (kid)". Even within his party, a section dubbed him a write-off.
He didn't help his cause when last month, he accused the Nitish Kumar government of plotting to poison his food.