Two goals in the first 20 minutes by Muhammad Shafiq Ghani gave Singapore a surprise 2-1 win over the Palestinians.
But the impoverished and restricted Palestinian team still topped Group C on a better goal difference over Tajikistan, who beat Oman 1-0 in their last game to claim the second qualifying spot.
Palestinian coach Abdalnasser Barakat said the conflict between Israel and Hamas in Gaza was constantly on the minds of the players.
"Football is a very popular sport at home and we want to make our people happy by doing well. Our people have a right to live peacefully and enjoy sport."
More From This Section
The Palestinians will next play Japan, who beat Nepal 4-0 to secure second place in Group D behind Iraq. The Iraqis ended their qualifying group with three straight wins -- hitting three goals past neighbours Kuwait in their final game. Humam Tarej Faraj scored two in the 3-0 win.
The group games end on Monday with China needing to beat Pakistan to avoid a humiliating exit from Group F. Second round games start on Thursday.