The War Elephants scored all three goals in the second half after a goalless draw in the first 45 minutes. Supachok Sarachat scored the first goal 11 minutes into the second half and Theerathon Bunmathan made it 2-0 with a penalty kick seven minutes later.
Supachok wrapped up the win with his second goal in the 71st minute to give the visitors three points.
The match played at the 80,000-seat Gelora Bung Karno Stadium but only some 10,000 Indonesian fans were at the venue to cheer their home team.
Thailand needed a win after the War Elephants were held to a goalless home draw by Southeast Asian rivals Vietnam in their first group game on Thursday in Bangkok. The Garudas also suffered a 3-2 defeat at the hands of Malaysia in their first match.
Nishino, who has faced criticism for going into the Vietnam game without a specialist striker, said on Monday his men needed to score goals in Indonesia.
"After the match with Vietnam, we have had time to prepare the team and I can say that we are getting better," said the veteran coach, who took Japan to the last 16 stages of the 2018 World Cup.