Midfielder Duong Thi Van scored the first goal for Vietnam just seconds before the first half ended with a header.
Thailand found the net in 52nd minute but the goal was denied as Thai defender Phonphirun Pilawan was ruled offside. However, striker Taneekarn Dangda headed in the equalizer in the 87th minute.
Coach Mai Duc Chung said it's a regret that Vietnam suffered an equalizer very close to the last minute.
Chung said his players had managed to stay focused after taking the lead, but a moment of distraction allowed Thailand to close the gap.
"But a draw was a fair result, each team deserves that one point," he said. "Vietnam were lucky as Thailand's several attacks at the beginning of the game lacked accuracy."
Vietnam's priority now is prepare for their game against Indonesia on Friday.
"If we play Thailand again in the final, we might achieve a more positive result."
Vietnamese women, who won the AFF Championship in August, are in Group B. Group A gathers Myanmar, Malaysia and the host, the Philippines.
Vietnamese women took home the gold medal at the previous SEA Games, where Thailand won silver.