Hoang Anh Tuan's men are not yet assured of qualification due to Iran's 3-2 loss to Australia but are in the driving seat to advance from the group stage.
It was a game of late drama in both halves; Nguyen Quoc Viet opened the score just before the break and Qatar equalised through a controversial penalty just seven minutes from full-time, before Truong sealed the victory in the 90th minute for Vietnam.
Qatar have not had a great start to the competition, having lost to Iran by a single goal. Vietnam, on the contrary, shocked Group B with a 1-0 win against favourites Australia.
Although Qatar did not play well against Iran, Tuan warned against complacency before the match.
Qatar dominated the first half, holding on to around 68% of possession, and had many dangerous attacks from the wings.
When the clock ticked down towards the interval, many Vietnamese fans thought about a draw in the first half, perhaps breathing a sigh of relief. However, they found themselves in a frenzy in the second minute of injury time.
From a counterattack, Truong pulled off a wonderful lobbed through ball for Viet, who went through on goal and struck the ball into the back of the net to score his second goal this competition, with the last kick of the half.
Vietnam were the better in the second half, as Tuan's midfielders created more dangerous chances than the opposition.
From an attack in the right wing, Al Rawi fell down inside Vietnam's penalty area and referee Akhrol Risqullaev pointed to the spot.
Al Rawi took the penalty he earned and beat Binh to bring Qatar back on level terms.
Vietnam did not capitulate after the equaliser but pushed forward strongly. In the 90th minute, Nguyen Duc Phu whipped in a free kick and found Truong, who scored with a backwards header.
The victory puts Tuan's team first place in Group B, but with Iran's earlier loss to Australia, all is to play for, and Qatar still cling to a slim chance of qualification.
Vietnam will qualify if they beat Iran or lose but score more than two goals. Equally, if Qatar beat Australia, then they qualify.