The 27-year-old British rider battled back from losing the opening race of the best-of-three final against Australian flyer Matthew Glaetzer to edge the next two.
It was his first world sprint title for five years and will send him to Rio in August as the man to beat.
"Those last two rides were tough," said Kenny who won the individual and team sprints at the same London velodrome in the 2012 Olympics.
"We were both knackered to be honest. It was a real slog, it wasn't the prettiest race of the day," he told reporters as his smiling girlfriend Laura Trott warmed up for her elimination race in the omnium.
Kenny was under pressure when Glaetzer took the opener by 0.002 of a second but responded superbly to keep the hosts at the top of the medals table with three golds, one of them won by Trott in the scratch race earlier this week.
It was Glaetzer's maiden world championship podium.
“To be close to that calibre of sprinter is really encouraging. I actually feel pretty pleased with that, it's a big achievement,” said Glaetzer.
"It's (silver) definitely not as nice as a gold, but that's added motivation to do everything I can in training and back home in Adelaide,” he said. “It's a great step, having this debut individual medal. But it just spurs me on to get one better.
Russian Denis Dmitriev took the bronze.
Colombia's Fernando Rendon Gaviria won the men's omnium title for the second year running, underlining his credentials for Olympic gold after an enthralling finale to the multi-discipline event that spans two days.
The 21-year-old, already tipped to become a multiple stage winner in the Tour de France, held off an incredible charge up the leaderboard by German Roger Kluge and Australian Glenn O'Shea to retain the rainbow jersey he won in Paris last year.
There was disappointment for Britain's Mark Cavendish as he finished sixth, putting in jeapoardy his hopes of securing a place in the British track team for Rio.
The 30-year-old, one of the most prolific stage winners in the history of the Tour de France, has interrupted his road season to return to the boards with the aim of finally winning a long-overdue Olympic medal.
Cavendish's pre-championships target was a podium place in the six-discipline omnium event but, after climbing to fifth following an impressive ride in the flying lap, he could make no further ground on the leaders.
Incredibly, after Kluge and O'Shea rocketed into contention by twice breaking away to gain a lap, collecting 40 points in the process, the first three were all locked on 191 points at the end.
Howver, Gaviria took the title because he finished ahead in the final dash to the line.
"After two days racing to have three guys on the same points, you can't get closer than that," said former world champion O'Shea.
The penultimate day's other gold medal went to Poland's Katarzyna Pawlowska in the women's points race, the third world title of her career.
Pawlowska steadily accumulated points, edging Canada's Jasmin Glaesser into the silver medal position with Cuba's Arlenis Sierra Canadilla finishing third.
Ireland's Caroline Ryan suffered a heavy crash near the end of the race and was taken off the track on a stretcher after receiving medical attention.
She went to hospital with a cut to her head.
The championships conclude on Sunday with an expected battle between Trott and American Sarah Hammer for the women's omnium.
They finished first and second at London 2012.
Golds are also up for grabs in the men's keirin, Madison and women's individual sprint.