The Malaysians were the better side in the opening stages but the Thais gradually become dominant in wet conditions.
However, it was Malaysia who went ahead after 28 minutes when Amri bin Yahyah's long-range shot beat Thailand goalkeeper Kawin Thammasatchanan.
Late in the first half, Thailand coach Kiatisak Senamuang replaced out-of-sorts Kirati Kaewsombut with Adisak.
Adisak immediately made his presence felt when he cancelled out Malaysia's lead with his first touch two minutes from the interval.
Malaysia regained the lead at the hour mark thanks to Safiq Rahim's strike.
Thailand equalised again after 72 minutes through Thai-Swiss Charyl Chappuis, and Adisak scored the winner in injury time.
"It was a fantastic and exciting match," said Kiatisak.
"Our players played very well. We were a goal down twice but our players kept fighting on.
"Although we have qualified for the semi-finals, we will do our best in the final group game against Myanmar."
Malaysia coach Dollah Salleh said: "It was a superb game and I am happy with my boys' performance. My boys played very well but could not finish off Thailand."
The Thai team will get one million baht for yesterday's win plus 200,000 baht for each goal they scored against Malaysia from the Football Association of Thailand.
Thailand have won the Asean title three times — the last in 2002. The Thais lost to Singapore in the previous final in 2012 as the Lions claimed a record fourth crown.