World champion Kulhavy produced an impressive ride on the seven 4.7-kilometre laps on a course overlooking the Thames estuary in Hadleigh Farm, east of London.
Kulhavy overtook Swiss world number one Nino Schurter, who took silver one second behind, at the top of the final uphill drag and kept his advantage in the descent before sprinting to the line.
Italian Marco Aurelio Fontana took bronze, 25 seconds off the pace.
"It was really hard. We went full gas all day," Kulhavy told the BBC. "I gave everything, all my energy. This was so important for me this year. I've now won everything, the World Cup, the world championship and now the Olympic title.
"This is the most special day in the sport for me. It was easy for the first half of the race but the finish was pretty hard and Nino was very strong so it was a big fight," Kulhavy then said.
"The last big climb I was there first and he was behind me, the last chance was in the chicane before the finish but I gave it everything.
"I was not so strong with two laps to go, my legs were hurting but I found some more power in the end and I had something left for the finish. It's amazing."
Absalon and Schurter were in the lead from the start, sprinting to the first short climb of the day, but the Frenchman's hopes vanished as he suffered a puncture in the opening lap.
Absalon was almost a minute down after just one lap and knew the gap was too big.
"After being an Olympic champion, there was no point in fighting for a 10th place finish," Absalon told reporters.
Schurter, Fontana and Kulhavy were joined by Spain's Jose Antonio Hermida Ramos and South African Burry Stander at the end of the third lap but the two could not sustain the pace.
Stander, however, made the connection again with one lap to go before cracking once more, leaving the leading trio battling it out for the medals.
Kulhavy, who based his whole season on the Olympics, followed Schurter when the Swiss attacked in the last lap, but the acceleration was fatal to Fontana's hopes.
The Czech rider and Schurter attacked each other several times halfway through the final lap but it was Kulhavy who had the last word.
Schurter had claimed bronze in Beijing four years ago when Absalon led a French one-two ahead of Jean-Christophe Peraud.
"It's hard to lose the gold so close, the Olympics was a big goal for me to win here. I was disappointed when i crossed the line but now I can be happy because it was a good race and Jaroslav was just a bit stronger in the last 200 metres," Schurter said.
"The first thing that goes through your head, though, is that you lost the gold medal."