Elsewhere in the Games, which end on Sunday, skateboarders soared in the Tokyo heat, open-water swimmers had to navigate elbows as well as fish, and a Japanese mayor grossed out the nation and prompted a rebuke from automaker Toyota for biting a softball player's gold medal.
U.S. men, who once dominated the 4x100 metres, failed to qualify for the final despite having two individual 100m finalists on the team. A ragged run, with poor changeovers and a shocking second handover, dragged them to a desultory sixth in their semi-final.
Carl Lewis, the superstar sprinter of the 1980s and '90s, called his compatriots' performance "a total embarrassment, and completely unacceptable".
China were the surprise heat winners, while Jamaica took the other semi.
In the 110m hurdles, world champion Holloway looked set to win until Parchment surged past him to add a gold medal to his London Olympic bronze in one of the biggest athletics shocks of the Games.
"The greatest feeling, the greatest feeling, I've worked so hard," the Jamaican said. "It's unbelievable that I caught this guy."
Sydney McLaughlin notched a huge world record in the women's 400m hurdles, besting fellow American Dalilah Muhammad as the super-fast track and new shoe technology continue to make a mockery of historical comparisons.
Canada's Andre De Grasse added gold in the 200m to a groaning collection of minor medals, while Kenya went one-two in the men's 800m and Peruth Chemutai made history for Uganda.
ELBOW AND FISH
Crouser, wearing shades and a hat with the U.S. flag on it, broke his own record in the shot put three times - only the third time that has happened - to grab gold with a mark of 23.30 metres.
He donned a cowboy hat afterward and celebrated with his countryman and silver medallist Joe Kovacs, draped in the Stars and Stripes. Crouser, from a family of throwers, held up a card reading "Grandpa, we did it, 2020 Olympic champion".
At the Sea Forest Waterway in Tokyo Bay, Carrington's gold in the women's kayak single 500 metres brought her overall medals haul at the Olympics to six, including a bronze in 2016.
She is now New Zealand's most successful Olympian. Fellow kayakers Ian Ferguson and Paul MacDonald, and equestrian athlete Mark Todd each have five medals.
"It's something I never thought I'd be able to do," she said. "It's amazing."
At nearby Odaiba Marine Park, however, the waters were more turbulent. Marathon swimmer Hector Thomas Cheal Pardoe of Britain got elbowed in the eye on the last lap, sustaining a cut and losing his goggles.
"I couldn't see anything, I thought my eye had fallen out in the water," he said in an interview after leaving the race. "I was going up to the lifeguard saying, 'My eye! My eye! Is it OK'."
Australia's Kareena Lee was hit on the chest by a fish the day before, after taking bronze in the women's marathon swim.
"I didn't know what it was at first and I was like 'woah'," she said.
Skateboarding continued to wow at its maiden Games, as the skaters sweated through temperatures of 32 degrees Celsius (89 degrees Fahrenheit) in the final runs, before taking selfies.
Australian Keegan Palmer glided to gold at Ariake Urban Sports Park in what looked like an effortlessly smooth ride packed with tricks in the men's park event. Brazil's Pedro Barros grabbed silver for his lightning fast run through the concrete bowl.
Less hip, Nagoya Mayor Takashi Kawamura suffered an online backlash for having feted softball pitcher Miu Goto the day before by pulling down his mask and putting her gold medal between his teeth.
It did not help that he was standing in front of a backdrop urging people to take proper COVID-19 precautions in a country looking to expand pandemic states of emergency as infections soar.
The hashtag #GermMedal was trending on Japanese social media - the words for germ and gold sound the same in the language.
Hometown giant Toyota Motor Corp called the mayor's stunt "unfortunate" and "extremely regrettable", a criticism to which his office did not immediately respond.
(Reporting by Mitch Phillips, Sudipto Ganguly, Omar Mohammed, Toshiki Hashimoto, Sakura Murakami, Mari Saito and Tim Kelly; Writing by William Mallard; Editing by Himani Sarkar) ((firstname.lastname@example.org; +81 3 4563 2749;))