Singh got 49 first preference votes, while the second Congress candidate bagged 45 votes in the 126-member state Assembly, its Principal Secretary and Returning Officer GP Das said.
All India United Democratic Front's (AIUDF) Aminul Islam, who polled 18 votes, lost. AIUDF is a partner of the UPA at the Centre and its 18 MLAs gave their second preference vote to the Prime Minister.
The Prime Minister was the only contestant for the first preference vote seat as the other parties did not put up any candidate against him.
The votes of all 78 Congress members and its ally Bodoland Peoples Front's 12 MLAs were found to be valid, Das said. Opposition Asom Gana Parishad and BJP, who have nine and five MLAs respectively, had earlier decided to abstain from voting.
The Congress now has five members out of seven in Assam in the Rajya Sabha. Polling was held from 9 am to 4 pm at the Assembly and counting of votes began at 5 pm.
The election process has to be completed before June 3 as per the Election Commission's May 13 notification.