City of Leeds diver Harding won his prize in the men’s 3m springboard final.
The 18-year-old was second in the morning’s preliminaries, only trailing China’s Junjie Lian, but it was Colombia’s Daniel Restrepo Garcia who eventually took gold in the final with 576.05.
As Lian buckled under the pressure, failing his first dive, Harding – who front loaded his final with his two hardest dives – delivered five clean performances to end on 559.50 with Russia’s Ruslan Ternovoi in third.
“I’m over the moon with silver,” said Harding. “It couldn’t have gone any better.
“Me and my coach discussed what I was going to do before the competition. My first dive was a new one and we thought we’d try it out and see how it went and it’s paid off.
“For the last dive I can do the four and a half but I chose not to do it here as training has been limited so we stuck with the easier one and it still went well. I knew the Colombian would come back because he’s got some big dives and the Chinese boy I just feel sorry for – it could happen to anyone, it could happen to me, but I’m pleased it went my way today.”
Leeds fighter Price will box for a gold medal in Buenos Aires after claiming victory in his flyweight semi-final.
The 18-year-old, who represents the Hunslet Club, defeated Ireland’s Clancy over three rounds, winning the bout on all five judges scorecards.
Price, the No 1 seed, will now meet Thailand’s Sarawut Sukthet in the final.
Olympic bronze medallist Nile Wilson, from Leeds, has pulled out of the upcoming artistic gymnastics World Championships with a finger injury.
British Gymnastics has announced that Brinn Bevan will take his place in the Great Britain squad for the event in Doha starting later this month.
Wilson, who has been troubled by injuries since winning bronze on the high bar in Rio two years ago, suffered his latest problem in training on the parallel bars on Friday.
British Gymnastics is hopeful he will be back to full competition fitness later this year.