Portuguese forward Goncalves opened the scoring in the 15th minute, before putting Chennaiyin two-up by converting a penalty in the 21st minute.
India international Anirudh Thapa scored in the first minute to set up Chennaiyin FC's 2-1 win over Jamshedpur FC in an Indian Super League match, in Vasco, on Tuesday.
Chennaiyin's defense was a tough nut to crack as Eli Sabia and Vishal Kaith came with crucial interceptions and blocks to deny Sunil Chhetri and Paartalu.
Adam Le Fondre smashed in a 75th-minute winner after Hernan Santana (45th) had cancelled Jakub Sylvestr's first goal.