Earlier, Dutch dominance of the men's sprint events continued as Jeffrey Hoogland (30) claimed a third successive 1km time trial world title.
Kopecky, runner-up in the Tour de France Femmes last month and now a six-time track world champion, made an early attack in the 100-lap race and then kept Australia's Georgia Baker safely at bay to win by eight points.
Britain's Neah Evans, the reigning champion, had challenged initially but got caught out of position when Kopecky took off with Baker in pursuit of a breakaway.
Evans ended up losing a lap to fall down the standings and had nothing left in the tank as Japan's Tsuyaka Uchino grabbed third place by taking the 10 points for the last sprint.
Kopecky also won the elimination race earlier in the championships and will be one of the favourites for the women's road race which concludes the championships on Sunday.
Hoogland joined his compatriot Harrie Lavreysen on two golds for the championships when he relegated two Australians to the bottom rungs of the podium with a masterful kilo ride.
Matthew Glaetzer had put himself in first place with a national record time of 58.526, but Hoogland, the last rider to go after qualifying quickest, completed his four laps of the Chris Hoy Velodrome in 58.222 to take gold.
Australia's Thomas Cornish was the third fastest.
Hoogland also won the men's sprint alongside Lavreysen and both of them will be going for a third gold in the keirin which reaches its conclusion on Wednesday.
Lavreysen retained his men's sprint world title on Monday.
The Netherlands are now second in the medals table with three golds compared to the four of Britain.
