Charyl Chappuis' penalty kick after 72 minutes and Kroekrit Thaweekarn's strike four minutes from time finished off the Tigers at a packed Rajamangala National Stadium.
The second leg will take place in Kuala Lumpur on Saturday as Thailand are chasing a record-equalling fourth title in the biennial event.
Thailand coach Kiatisak Senamuang was a player of the three winning sides. He has never lost to Malaysia as a player and a coach.
His men also beat Malaysia 3-2 in Singapore in the group stage of the current campaign.
"Malaysia played very well and their defence was solid in the first half," said Kiatisak.
"It was an exciting match. I am pleased with the win but our mission is not yet complete. Our aim is to win back the trophy.
"We have a 2-0 lead and the atmosphere at the 80,000-seat stadium in Kuala Lumpur will be a big test for our young players. But the Malaysia team will be under pressure too."
Malaysia coach Dollah Saleh said: "In the first half we played very well in defence but in the second half, I don't know what happened and the Thai played very well.
"At home, we will try our best. It is not easy when we are 2-0 down, but anything can happen in football especially when we play at home. I am still believe that we can do better in Kuala Lumpur."
At Rajamangala, Malaysia gave the War Elephants a scare in the opening minutes, forcing Thailand goalkeeper Kawin Thamsatchanan to make a couple of good saves.
But the Thais soon found their rhythm and began piling the pressure on Malaysia.
Kroekrit, Sarach Yooyen and Chanathip Songkrasin squandered several chances with goalkeeper Mohd Farizal in good form.
After 41 minutes, striker Adisak Kraisorn went clear but his shot was cleared off the line by Malaysia defender Muhammad Zabir Azmi.
Thailand were dominant in the second half and finally got their first goal when they were awarded a penalty after Adisak was tripped in the area.
Thai-Swiss midfielder Chappuis made no mistake from the spot.
Thailand got a two-goal cushion thanks to Kroekrit's close-range shot in the 86th minute.
Thailand will get one million baht in bonus for last night's win from the Football Association of Thailand.
The Thais are expected to receive more than B20 million in bonus and prize money if they lift the trophy on Saturday (December 20). Bangkok Post