Lavreysen added to the men's one-kilometre time trial and team sprint gold medals won earlier this week.
Untouchable in the sprint, the five-time defending champion won the main event on Sunday to hammer home his dominance on the final day of competition at Ballerup in the suburbs of Copenhagen.
The 27-year-old easily beat compatriot Jeffrey Hoogland with whom he won the team sprint on Wednesday. Japan's Kaiya Ota was third.
Lavreysen this week overtook France's Arnaud Tournant's 14 world championship titles between 1997 and 2008.
The king of sprinting now has six world team sprint titles, six individual sprint gold, three in the keirin and one in the one-kilometre time trial.
The five-time Olympic champion's next big goal remains Los Angeles 2028, where he aims to beat British rider Jason Kenny's record of seven Olympic titles.
In the women's event, home hope Julie Leth, competing in the very last race of her career, struck gold amid an electric atmosphere in a packed velodrome.
The 32-year-old, winner of the Madison on Saturday, won the points race ahead of Belgian star Lotte Kopecky and Ireland's Lara Gillespie.
Japan's Mina Sato beat Dutch rider Hetty van de Wouw to win the women's Keirin with Britain's Katy Marchant third.
