After Julie Bresset of France won the six-lap women’s race on the 4.7-kilometre route on Saturday, 2004 and 2008 winner Absalon withdrew with a mechanical problem while trailing a front group which included 2011 world champion Kulhavy.
The pace was relentless but the Czech had enough strength to win a sprint finish ahead of Nino Schurter of Switzerland, with Italy’s Marco Fontana third.
“This is the best moment of my life because the gold medal is the pinnacle of the sport,” Kulhavy said.
“I was really happy because last year was amazing, but I did everything for this race. The training was really hard and I didn’t have such a good season as last year, I was really tired and I had some small health problems. So I am happy I won.”
Schurter was content.
“It was a great race,” he said. “I was attacking from the first lap, always riding in the first two positions. “I have to be happy with silver. Kulhavy was super-strong, he deserved it. I would say it was a big fight, a big show for our sport and now I have to be happy about my silver.”
Absalon’s defence of the title he won in Athens and Beijing ended in a whimper.
He said: “I didn’t have any chance to reach the podium.”
There was a French winner on Saturday, with Bresset claiming her nation’s first Cycling gold of the Games.
Bresset, the 2011 world under-23 champion, said: “I loved being on the circuit. I used technique and decided to go ahead quite soon.
“I was a bit scared to be right at the front but actually, being right at the front, I wasn’t tired and I felt good.
“My training paid off and I was ready for D-Day.”
Sabine Spitz of Germany was the defending champion, but had to settle for silver.
The 40-year-old had a battle with Georgia Gould of the United States, who finished with bronze, the medal Spitz won in Athens.
Spitz said: “It was always a bit back and forth with Georgia. In the last lap it was clear I had to give everything and I had to give 100%. The silver medal is the one that was missing in my collection.”