Sebastien Haller netted his seventh league goal of the season after taking advantage of good work from Ante Rebic and Luka Jovic to convert from close range with only 11 minutes gone.
Rebic then got on the score sheet as he doubled Frankfurt’s tally just after the half-hour mark when he guided his header into the top corner.
Substitute Nicolai Muller completed the rout for the visitors by nodding home in the final minute.
Stuttgart’s seventh league defeat from their opening 10 matches leaves new manager Markus Weinzierl, who replaced Tayfun Korkut last month, still awaiting his first point. Indeed, Stuttgart have now conceded 11 goals without scoring in their last three games.
Frankfurt, winners in seven of their last eight matches in all competitions, move up to third in the table, having played one more fixture than their rivals.