The 25-year-old, co-captain of the squad, claimed victory in a season’s best of 7.46 seconds to beat American Jarret Eaton by one-hundredth of a second.
Pozzi, who has overcome serious injury problems, added the title to his European Indoor gold which he won in Belgrade 12 months ago.
He is eyeing the 2020 Olympics in Tokyo after previous disappointments on the biggest stage.
“I honestly believe I have everything it takes to be the best hurdler in the world and I wouldn’t have stuck it out if I didn’t genuinely believe that,” he said, as Great Britain won seven medals at the championships.
“And I’m on the right track now so it’s just about keeping on the right track to Tokyo. I can’t even begin to describe the feeling. I’m absolutely over the moon to do that. To win my first global (title) is one thing but to do it in Birmingham is so much better.”
Pozzi had finished fourth twice in the World Indoors – in 2012 and 2014 – and victory follows his recovery from persistent injuries.
He added to Shelayna Oskan-Clarke’s bronze medal in the 800m. British co-captain Oskan-Clarke came third in the final in one minute 59.81 seconds.
“I’m happy to have got a medal, I really had to dig deep for that one,” she said.
“I’ve put a lot of work in so I knew it was in there.
“It’s taken a while to get back into a final but you have to be positive and hope it will happen.”
The women’s 4x400m relay squad of Meghan Beesley, Hannah Williams, Amy Allcock and Zoey Clark were involved in drama that had a rewarding outcome.
They were promoted to bronze after Jamaica were disqualified for changing lanes for the handover of the baton, before being thrown out themselves for pushing.
But the British quartet were reinstated in bronze after an appeal, while the men’s 4x400m squad came sixth.