In Godda, BJP candidate Amit Mandal defeated Rashtriya Janata Dal (RJD) candidate Sanjay Yadav by over 34,000 votes.
The Jharkhand Mukti Morcha (JMM) candidate came in third position.
In Panki, Congress candidate Devendra Singh alias Bittu Singh defeated JMM candidate Kuswaha Sashibhushan Mehta by over 6,000 votes.
The ruling BJP came third in Panki.
The outgoing state BJP president Rabindra Rai admitted that "some mistakes" were made and the party could not reach out to voters in Panki.
The by-polls for the two seats were necessitated following the deaths of BJP MLA Raghunandan Mandal Godda and Bidesh Singh of the Congress from Panki.