The Bhutan team secured the tie 3-1 on aggregate after it also won the first leg in Colombo last week.
Two goals from Checho Gyeltshen on either side of Zohar Mohamed Zarwan's strike saw 209-ranked Bhutan through in front of 20,000 fans.
Timor-Leste accompanied Bhutan into the next round by beating Mongolia 1-0 in Ulaan-Baatar for a comfortable 5-1 aggregate win.
India drew 0-0 with Nepal in Kathmandu to go through 2-0 on aggregate.
Elsewhere, Cambodia drew 1-1 at Macau to secure a comfortable 4-1 agregate win while Chinese Taipei accounted for Brunei 2-0 to win through 2-1 on aggregate.
The second leg of the tie between Pakistan and Yemen was postponed.