Australian track cyclist Matt Richardson has finished second and compatriot Matt Glaetzer is third in the keirin final behind Dutch great Harrie Lavreysen.
Richardson was unable to pass Lavreysen on the final straight after Glaetzer hit out first in the final, with the other three riders crashing on the last lap.
It is Richardson's third medal at the Paris Olympics, after he also finished runner-up to Lavreysen in the sprint.
After a run of fourth-placed finishes at his previous three Olympics, Glaetzer has won an individual medal for the first time at his farewell Games.
Glaetzer and Richardson also won bronze in the team sprint.
There was some drama after the final, with Malaysia's Australian coach John Beasley arguing heatedly with officials.
Malaysian rider Muhammad Sahrom, who was involved in the crash, was relegated to last place.
British rider Jack Carling and Japan's Shinji Nakano did not finish as a result of the crash.
Lavreysen swept the men's sprint events, with the Netherlands also dominating the team sprint.
Richardson handed Lavreysen a rare loss when the Australian beat his Dutch rival in their semi-final.
But Lavreysen was imperious in the final, taking the lead at the perfect moment and holding off Richardson at the finish.
He is the first rider to sweep the men's sprint gold medals since British great Sir Chris Hoy in 2008.
Also on the last day of Olympic competition, Australian Georgia Baker is second with one event left in the women's omnium at the Saint-Quentin-en-Yvelines velodrome outside Paris.
New Zealander Ellesse Andrews beat German Lea Friedrich to win the women's sprint gold after also taking out the keirin.