Kopecky, who won two golds on the track during the championships, burst from a small group of leaders on the final lap of the city circuit and powered to victory.
Denmark's Cecilie Uttrup Ludwig initially managed to go with Kopecky but she could not cope with the Belgian's speed.
Kopecky cruised over the line at the end of the 150km trek, celebrating her first world road title.
Dutchwoman Demi Vollering, who won the recent Tour de France Femmes, pipped Uttrup Ludwig to the line to take silver.
Kopecky's hat-trick of golds from the Glasgow world championships included her titles in the elimination and points races at the Chris Hoy Velodrome where she also won a bronze medal in the omnium.
The final action from the 11 day championships that included virtually every cycling discipline and 46 world titles up for grabs, proved a fitting climax to a two-wheeled festival with thousands lining the streets of Glasgow.
Beginning near Loch Lomond, the race was always likely to really ignite once the riders arrived for the six 14.3km circuits of the city alongside the River Clyde.
Swiss rider Elise Chabbey was the first to show her hand with an attack that caught out the bunch and she extended her advantage to more than a minute as the laps ticked down.
Kopecky was frustrated at times at being forced to lead the chasers, gesticulating at one point and slamming on her brakes.
But they gradually reeled in Chabbey and at the start of the final lap her time at the front was over.
Britain's Lizzie Deignan, world champion eight years ago, hit the front with Christina Schweinberger but that was shortlived as Uttrup Ludwig and Kopecky with Vollering also in the mix despite shaking off her leg with cramp.
Kopecky's next attack proved decisive as she went clear with six kilometres remaining.
It seemed audacious but there was no stopping her as she crested the last climb and soloed to victory.
"An amazing year and a hard year," an emotional Kopecky told Eurosport. "I don't know what makes me keep me pushing, I don't know what I was thinking, but this is a dream that came true.
"To win three gold medals here is too crazy for words."
Kopecky's win followed compatriot Remco Evenepoel's gold medal in the men's road individual pursuit.
The final day's other action took place on the BMX racing circuit where Britain's Olympic champion Bethany Shriever took gold ahead of Laura Smulders of the Netherlands.
The men's podium was filled with French riders as Mahieu Romain won gold ahead of Arthur Pilard and Joris Daudet.