Van Su opened the scoring in the 30th minute with a curling strike before world No.67 India equalised in the 52nd minute via Sanfida Nongrum in Wednesday's clash at HBF Park.
The 36th-ranked Vietnam were hot favourites, and anything other than a victory would have put a big dent in their hopes of qualifying for the quarter-finals for a second successive time.
Van Su came close to nabbing the winner on several occasions, and she eventually broke through in the fourth minute of extra time when she put away Vu Thi Hoa's smart cross.
Vietnam's players piled on top of the cramping Van Su after the goal went in, with the three crucial points putting them second in group C behind Japan, who beat Taiwan 2-0 earlier in the day.
Vietnam's pace proved hard to handle for India in the first half, with the lightning-quick Nguyen Thi Bich Thuy proving particularly tricky.
Bich Thuy put India on notice in the 14th minute when her 24-yard strike hit the crossbar.
The 31-year-old had several other good looks on goal - but some of the best build-ups went unrewarded after Bich Thuy fell foul of the offside trap.
Vietnam enjoyed 63 percent possession in the first half, and they hit the lead in the 30th minute via a beautiful curling strike from Van Su.
The second half began with a bang.
Vietnam were celebrating their second goal in the 48th minute after Thai Thi Thao was able to poke the ball in on her fourth attempt from a mad goalmouth scramble.
But VAR intervened to rule Thia Thao had been offside.
Then just four minutes later India notched the equaliser as substitute Nongrum unleashed a shot that brushed the goalkeeper's fingertips and went in.
Vietnam came close to regaining the lead in the 76th minute when Van Su beat three defenders on her way into the box - only for the goalkeeper to block her low shot.
But when her moment of truth came in the 94th minute, Van Su made no mistake with the finish, sending the small crowd of 1961 fans wild.
