Verstappen had started 16th but an audacious two-stop strategy helped him force his way up the field.
And on a fresh set of tyres, he homed in on Kimi Raikkonen in third place, overtaking him on the final lap to claim a dramatic podium spot.
But his joy was short-lived as the stewards decided he had cut the corner and gained an advantage, relegating him back to fourth with a five-second time penalty.
The Dutchman, 20, was furious with the decision and even called on fans not to come back to the US Grand Prix next year as a form of protest.
“We had a great race but of course with those stupid decisions you really kill the sport,” Verstappen said.
“I really hope the fans didn’t like the decision and hopefully next year they won’t come.”
He added: “It’s not good for the sport and they have to be really clear on the rules that it’s not allowed everywhere.”
Verstappen’s team boss Christian Horner was similarly angry, especially having seen his other driver Daniel Ricciardo retire with an engine failure.
“There’s been cars going off track all day today and there’s been no action at all so I think it would be unbelievably harsh to give Max a penalty for that,” Horner said.
“It just doesn’t feel right.
“It’s wrong. We’ll have a look at it but for that was fair, hard racing.
“That’s a bad judgment by the stewards.”
He added: ”It is an appalling decision.
“They have robbed all of the fans here.
“It was a great Grand Prix and they have screwed it up.”
Mercedes’ Niki Lauda waded into the debate by saying: ”They shouldn’t intervene in situations like that. It was a normal overtaking move. You can’t be more stupid than that.”