Thomas held off a furious challenge from his rivals on the last lap to finish with a total of 149 points, two more than Gate.
Albert Torres of Spain, who led coming into the last of the four events that make up the omnium, had to settle for bronze.
In the men's sprint event, Russia's Denis Dmitriev showed nerves of steel to beat Dutchman Harrie Lavreysen in the final and claim his first world championship gold, with New Zealand's Ethan Mitchell securing the bronze.
The were spectacular crashes as the Belgian team of Jolien D'Hoore and Lotte Kopecky swept to a hard-fought win in the first-ever women's Madison event at the world championships. Britain took silver and Australia bronze. A dominant display by American Chloe Dygert gave her gold in the women's individual pursuit, the 20-year-old comfortably beating Australian Ashlee Ankudinoff by over six seconds. Dygert's U.S. team mate Kelly Catlin beat Rebecca Wiasak to take bronze.
Earlier in the day, Russia claimed two medals in the women's 500m time trial event. Daria Shmeleva won gold and Anastasia Voynova bronze with Germany's 2012 Olympic team sprint champion Miriam Welte taking silver. (Writing by Philip O'Connor in Stockholm, editing by Ed Osmond)
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