In 1949–1951, Baruah's political career began as a member of the Constituent Assembly.[2] He is now chiefly remembered for his alleged proclamation regarding Prime Minister Indira Gandhi, in 1974 "India is Indira. Indira is India."[3] However, he later parted ways with her and joined Congress (Urs), later renamed as Indian Congress (Socialist). He was the Governor of Bihar from 1 February 1971 to 4 February 1973. He died in New Delhi. He is the first and only Assamese to be elected as a president of Indian National Congress.
Baruah was a noted poet as well. His collection of Assamese poems, Sagar Dekhisa (সাগৰ দেখিছা), is still very popular. He was the elder brother of famous Assamese poet Nabakanta Barua.