By Gabriel Tan in Bangkok
The Red Warriors, who won the competition back in 2008, were expected to comfortably see off their opponents and despite being dominated in the first half, it was them who led at the break thanks to Le Tan Tai's 35th-minute header.
However, Myanmar came back strongly in the second half, with attacking midfielder Kyi Lin in particular causing all sorts of problems to the Vietnam backline, and it was he who earned a point for his side six minutes before the hour mark when he converted a penalty he had won.
Nonetheless, according to assistant coach Hoang Anh Tuan, Saturday's draw does not necessarily spell the end of their semi-final prospects, even with two tricky games to come against Philippines and Thailand.
"We are satisfied with the result today [Saturday]," he said in the post-match press conference. "Drawing the first game is not such a bad result.
"In football, sometimes you find yourself in situations where you make mistakes.
"But drawing the first game? No problem."
Anh Tuan also reiterated team manager Ngo Le Bang's comments on Friday that Vietnam were aiming to make the final at the very least, and revealed they will now turn their attentions to getting the necessary results in their next two matches.
"Of course, our target is still to go all the way," he added.
"We still have two more games and we must now prepare for them and do our best.
"But I think today [Saturday] we played very well."
Myanmar team manager Tin Myint Aung hailed his players for their gritty display against one of the pre-tournament favourites, and expressed his belief that their ploy to hit their opponents on the counterattack had worked.
"I would like to express my appreciation for the players," he said. "This was their best performance.
"All the players are trying very hard and I'm very happy with this result.
"We have learnt a lot from the last few years and were aware Vietnam is stronger than our team. That's why we discussed about defending well and playing on the counterattack - that is our plan.
"Our strategy is to be compact in defence and be fast on the counter - this is now our weapon and that's why we are playing this way.
"Of course, I'm very satisfied with one point."
Myanmar will be looking to cause another upset on Tuesday when they take on Group A hosts Thailand, while Vietnam will hope to bounce back against Philippines.
ESPN STAR Sports will broadcast all 18 matches with the most extensive online coverage on the AFF Suzuki Cup. Check espnstar.com (espnstar.my or espnstar.co.id) for local TV listing & breaking news. Follow us on Twitter @espn_star (or @espnstarmy, @espnstarid) for the latest updates from Kuala Lumpur and Bangkok.