Belgian Mels - already World Cup champion - fell to the back of the pack in the early stages, while Austria's Daniel Federspiel was knocked from his bike by Frenchman Kevin Miquel on the first climb.
Mels remained third out of four finalists for much of the rest of the race, with Miquel looking well-placed to comfortably cross the line in first.
However, Miquel was closed down by Sweden's Emil Lindgren in the approach to the final bend.
The two collided, opening the door for Mels to ease through and take the gold medal, and the 22-year-old acknowledged the fact he had been fortunate to win the race.
"I had a very bad start and I was already trying to keep up the pace and try to pass Emil because he had quite a big gap to Kevin," Mels commented.
"At the end, Lindgren just came up the inside to Kevin and they crashed and I had the way open to the finish line.
"It's crazy. I was waiting for the sprint because I didn't have a very good start, but this is above my imagination at the moment, so I'm really happy."
Asked whether the win compared to his triumph at the World Cup earlier this year, Mels added: "This is way above it. You have the rainbow jersey and you can wear it the whole year. You work so hard for it the whole year and then the hard work pays off."
There was another double winner in the women's event, which saw Kathrin Stirnemann lead to home a Swiss one-two to add the World Championship to her World Cup crown.
Stirnemann and compatriot Linda Indergand led from the start and never looked like being caught.
The advantage left Jenny Rissveds of Sweden and Norway's Ingrid Boe Jacobsen to battle it out for bronze, with the latter coming out on top following a collision between the two.
"It's unbelievable," said Stirnemann. "I tried to save as much energy as I could in the heats before and give it everything in the final.
"I can't believe it. It's a dream come true. I've won everything I could this year. It's the best day I think."