BJP's Amit Mandal defeated RJD's Sanjay Yadav by 34,551 votes on the Godda seat, election officials said.
From Panki, Congress's Devendra Kumar Singh defeated JMM candidate Kushwaha Shashibhusan Mehta by 3,558 votes, Returning Officer Albert Bilung said.
The two seats fell vacant after the demise of Bidesh Singh (Congress-Panki) of heart attack on March 28, and Raghunandan Mandal (BJP-Godda) of illness on January 3.