The Golden Star Warriors had almost seventy per cent of possession and twenty shots per goal but could not find a way to pierce Singapore's defence.
Park Hang-seo made eight changes to the starting line-up from the 3-0 win against Malaysia on Tuesday in Hà Nội.
Veterans Đặng Văn Lâm, Quế Ngọc Hải and captain Đỗ Hùng Dũng stayed in the starting 11.
On the other side of the pitch, Singapore's Takayuki Nishigaya started Hassan Sunny in goal, replacing Hafiz Nor, and Shawal Anuar with Ryhan Stewart and Irfan Fandi in defence.
The first dangerous chance of the match came to Việt Nam in the 11th minute when Nguyễn Văn Quyết's shot forced Hassan Sunny to parry. The rebound reached Phạm Tuấn Hải, but his shot went straight at Sunny.
Sunny was troubled again six minutes later when Vũ Văn Thanh fired a vicious shot outside the box, but the Singaporean keeper made a simple save
Deep in their half, Singapore looked for opportunities on the counter. In the 26th minute, from Shakir Hamzah's left-wing cross, Ilhan Fandi tried a shot from outside the box, but the ball went wide.
Việt Nam replied just minutes later when Văn Quyết seemed to have capitalised on a Singaporean defender's mistake. From 25-metres, the Hà Nội FC captain's shot went way over the bar.
Just before the break, Văn Thanh was freed in the right wing by Hùng Dũng and crossed inside the box. The powerful cross hit a Singapore defender and rebounded to the side netting.
Heavy firepower was brought on by Park after the break, in the form of superstars Nguyễn Quang Hải and Phan Văn Đức, who replaced a fatigued Hùng Dũng and a dismal Châu Ngọc Quang.
The changes, however, did not work immediately. Nguyễn Hoàng Đức and Nguyễn Tiến Linh were brought on in the 58th minute.
Just four minutes after Đức and Linh were subbed on, the two combined and found Sunny's net. However, the goal did not stand because the referee paused the match after Văn Thanh was brought down.
Seconds later, Việt Nam won a free kick near the six-yard box. But from his favourite position, Quang Hải tried a lobbed shot that went just wide.
Tiến Linh, who Ngọc Hải jokingly compared to Argentina's Lautaro Martinez for his missed opportunities, had around five clear chances after he was subbed on.
In the 65th minute, Linh could have won it with a belter for Việt Nam, but his volley outside the box was bravely saved by Hassan Sunny, who went down injured later.
Ten minutes later, it was Linh again who had time and space on his side, but the Bình Dương striker's shot was too rushed and not on target.
Luck was not on Việt Nam's side again in the 84th minute, when Hoàng Đức's 30-metre shot beat Hassan Sunny, but the effort hit the post to the agony of the Vietnamese supporters at Jalan Besar Stadium.
Việt Nam had two more chances to win the game, but Tiến Linh squandered both and the match finished 0-0.
With this result, Việt Nam's position at the top of Group B still stands, but they are not yet qualified for the knockout stage.
In the unlikely event of the Golden Star Warriors losing by seven goals at home to already-eliminated Myanmar next Tuesday, as well as a draw in the match between Singapore and Malaysia happens, Park's team will be eliminated.
However, a win is needed for Việt Nam to avoid trickier opponents in the knockout stage, as well as rebuild confidence for the squad./.