Lavreysen flew around the final corner to beat Australia's Matthew Richardson, who took the silver.
The powerhouse also won the team sprint and sprint, repeating his feat from Tokyo where he could only manage a bronze in the keirin.
Australia's Matthew Glaetzer was third.
The race finale was somewhat overshadowed by a high-speed crash just before it involving Malaysia's Muhammad Shah Firdaus Sahrom, Japan's Shinji Nakano and Britain's Jack Carlin who were all sent tumbling across the track.
Sahrom slid over the line but was relegated for causing the accident. All three riders eventually managed to walk away after treatment.
If Lavreysen has dominated the men's events, New Zealand's Ellesse Andrews reigned supreme in the women's and completed an incredible week on Sunday by winning the sprint gold.
Andrews outclassed Germany's Lea Freidrich in the final, winning 2-0, to become the first woman from New Zealand to win the discipline at the Olympics, having also won the keirin and finished with the silver medal in the team sprint.
"Honestly, this has exceeded all my expectations," Andrews, whose keirin gold on Thursday was the first Olympics track title in 20 years for New Zealand, told Eurosport.
"I knew what my strengths were and put it out there."
Britain's sprint world champion Emma Finucane beat Dutch rider Hetty van de Wouw to take the bronze -- the 21-year-old Briton's third medal from her first Games.
Lavreysen has been in a league of his own all week, although he was beaten into second place by Richardson in the semi-finals of the keirin.
Come the final it was business as usual for the former BMX rider they call The Beast, however, as he was roared home by an orange army of Dutch fans in the stands.
He has emulated British sprint greats Chris Hoy (2008) and Jason Kenny (2016) in winning all three sprint golds on offer at a single Olympics and now has five in total.
