With the visitors pushing for a second goal, the hosts, without injured top striker Erling Haaland, struck against the run of play when Giovanni Reyna latched on to a pinpoint Raphael Guerreiro cross to chip the ball over the Stuttgart keeper.
But a mistake by Guerreiro on the edge of the box in the 53rd sent Wamangituka through for his seventh goal of the campaign.
Philipp Foerster, in his second start for Stuttgart, made it 3-1 on the hour before teenager Tanguy Coulibaly added another goal three minutes later with Dortmund’s defence in complete disarray. Nicolas Gonzalez added the fifth in stoppage time.
Dortmund, who have now gone three league games without a win, slip to fifth place on 19 points, while Stuttgart move up to sixth on 17.