The 32-year-old Hammer, winner of five individual pursuit world titles in her illustrious career, steered rising stars Kelly Catlin, Chloe Dygert and Jennifer Valente to victory over a Canadian quartet who hung on grimly but could not keep up.
“It’s very emotional, this is my eighth world title but I’ve been waiting my whole career to get a first team title,” Californian Hammer told reporters at the London velodrome where they had beaten world champions Australia in the semis.
“Doing it in a team there’s nothing like that. It’s the fact that there is no one individual more important than another. It’s one unit all working together.”
Scratch race champion Laura Trott helped Olympic champions Britain clinch the bronze medal with victory over New Zealand.
But the cheers for Trott were nothing compared to the deafening roars for Dibben who won the 160-lap points race at the death to double the host country’s gold-medal tally.
The often puzzling tactical race, which awards points for intermediate sprints every 10 laps, looked as though it was heading to Austria’s Andreas Graf.
Dibben then won the penultimate sprint and, knowing he needed to win the final one to pip Graf, produced a sensational burst of raw acceleration to snatched it.
“Winning a world title in your home country — it doesn’t get much better!” Dibben, who suffered heartbreak a day earlier when Britain were pipped to team pursuit gold by Australia, said before slipping on his first rainbow jersey.
Italy’s Filippo Ganna won the men’s individual pursuit, beating Domenic Weinstein who had been hoping to land a third gold of the championships for Germany.
Andy Tennant won an all-British battle for bronze over Owain Doull to take his first individual world championship medal.
World record holder Anastasiia Voinova of Russia retained her 500m time trial title with a blistering ride, clocking 32.959 seconds to add the TT gold to the women’s team sprint title she claimed on Wednesday.
Britain’s Mark Cavendish, juggling his road schedule to try and qualify for the Rio Games where he hopes to earn a first Olympic medal, completed the first three events of the omnium in seventh place.
Tour de France sprint king Cavendish moved up the leaderboard when he finished second in the elimination race, although he faces a crucial day on Saturday.
Cavendish has been given a podium target in the omnium to snatch a place on the Olympic track team.
Colombia’s Fernando Gaviria Rendon leads the standings from Italian Elia Viviani ahead of Saturday’s one km time trial, flying lap and points race.
(Reporting by Martyn Herman; Editing by Ken Ferris)