Dressel, who won the men’s 50m freestyle and 100m butterfly golds earlier in the evening, swam the opening leg before Simone Manuel touched the wall at three minutes, 19.60 seconds to seal America’s win.
The victory in a world-record time capped an incredible night for Dressel who had earlier won the 50m freestyle and 100m butterfly finals within half an hour of each other.
It is thought to be the first time a USA swimmer has won three golds medals in one day at a world championships.
“I haven’t had much time to think tonight,” said 20-year-old Dressel. “It’s back to back events, it’s physically demanding and mentally it’s even more straining.”
The time shaved more than three seconds off the previous record the US team set two years ago in Kazan.
The Netherlands took silver at 2.21 secs back while Canada claimed bronze at 3.95.
Dressel has now won six golds in Budapest. He has three individuals titles, including the 100m freestyle, plus victories for the USA in the men’s 4x100m freestyle, mixed 4x100m medley and mixed 4x100m freestyle relays.
He could win a seventh gold in the men’s 4x100m medley relay on Sunday.
“I have 24 hours to my next swim, so I’ll give myself 30 minutes tonight to let it sink in a bit and then it’s time to refocus for the next event tomorrow,” said Dressel.
His haul overshadows even compatriot and freestyle queen Katie Ledecky, who leaves Budapest with five golds and a silver.
“He’s incredible, he’s just a great athlete,” said Ledecky about Dressel after her victory in the women’s 800m freestyle final on Saturday.
“The way he goes about his racing, it’s really impressive.
“He’s really fired up Team USA with his performances in the water this week.”
Dressel’s relay team-mates paid tribute to his jaw-dropping performances.
“It’s unbelievable man,” said Nathan Adrian, who swam America’s second leg on Saturday.
“It’s unheard of until now — everything is impossible until someone does it.”
Simone Manuel, the world and joint Olympic 100m freestyle champion, said Dressel deserves his success.
“He’s an amazing athlete and he knows how to race,” said Manuel. “He is trained for it, it that’s how we all have our successes.
“Sometimes it comes out as a surprise when you work hard and you get what you achieve, but you worked hard for it.”
Mallory Comerford, who swam the third leg, said Dressel’s performances in the individual finals had inspired the relay team.
“It’s amazing to know that he’s leading us all off,” said Comerford.
“It’s inspiring to watch him swim and do well, it brings conference to the relay.”