Japan, four-time champions who last won the Asian Cup in 2011, were shocked into action when Vietnam took a 2-1 lead before the Samurai Blue cut their south-east Asian opponents down to size with two goals just before halftime.
Vietnam's initial resistance when the game kicked off lasted all of 10 minutes before Japan scored, with Minamino being in the right place at the right time to pounce on a rebound and guide it through a crowd of players into the net.
But Vietnam shocked Japan with an equaliser five minutes later from a corner when Nguyen Dinh Bac - running away from goal - directed a glancing header that looped over the keeper and into the net at the far post.
As the game opened up and with both sides creating chances, it was Vietnam who took the lead from another set piece when Bui Hoang Anh headed the cross to the far post where Japan keeper Zion Suzuki failed to deal with it and Pham Tuan Hai fired home.
The goal sparked wild celebrations and Vietnam coach Philippe Troussier, who is no stranger to Japan having guided them to the title in 2000, allowed himself a wry smile when they went 2-1 up.
But their lead did not last long either as Minamino scored again before halftime when he was released into the box by skipper Wataru Endo, with the AS Monaco midfielder guiding a low shot past the keeper.
Japan rediscovered their urgency and quickly restored their lead just before going in for the break when Keito Nakamura scored a fantastic goal from the edge of the box, curling his shot into the top corner past the keeper's outstretched hand.
The goal took the sting out of Vietnam and they failed to muster attacks in the second half as Suzuki cut a lone figure in Japan's half with most of the action on the other side of the pitch.
Japan then put the game out of reach when Ayase Ueda scored their fourth in the 85th minute before they saw out the game, sealing the three points for Hajime Moriyasu's side.
