The floor test was overseen by acting Speaker and Bharatiya Janata Party MLA Michael Lobo, according to Hindustan Times.
After winning the trust vote, Sawant appealed all the members to join hands with him to ensure that developmental work reaches every nook and corner of the state.
Governor Mridula Sinha had convened a special session of the Assembly at 11.30 am to enable Sawant to prove his majority in the House, an official said.
The strength of the 40-member House was reduced to 36 due to the death of chief minister Manohar Parrikar and BJP MLA Francis D’Souza, and the resignations of Congress MLAs Subhash Shirodkar and Dayanand Sopte.
The Congress, which is the single largest party with 14 MLAs, had also staked claim to form the government.
Sawant was sworn in as the new chief minister of Goa just before 2 am on Tuesday, after hectic parleys between the saffron party and its allies to put a new government in place in the state.
The governor also administered oath to 11 other ministers, including those from BJP’s allies MGP and the GFP.
(With PTI inputs)