Lukas Rohan from the Czech Republic took silver with Germany’s Sideris Tasiadis, who finished runner-up in 2012, getting bronze.
Savsek paddled through the difficult course straight after his German rival in 98.25 seconds, making him the only finalists to complete the course in under 100 seconds.
That run brought an end to the dominance of Slovakia and France in the event in which they had won every gold medal since the 1996 Atlanta Games.
“It’s a nice step up from world champion to Olympic champion. I am really proud to achieve this,” Savsek said.
“The course was pretty hard today,” he added at a news conference wearing the gold medal presented to him by French three-times Olympic slalom champion Tony Estanguet.
Slovakian paddler Matej Benus, who was aiming to better his silver in Rio de Janeiro five years ago, ended sixth with Martin Thomas from France fifth.
Cloudy weather at the Kasai slalom centre next to Tokyo Bay made conditions easier for competitors after they battled through baking sun and warm water in the heats on Sunday, but the hot Japanese summer still made the going tough.
“The heat today was not as big a problem, it was much better, but the water is still hot,” Savsek said.
Australia’s Jessica Fox, who will attempt to take the women’s kayak title Tuesday, had described the course as being like “bath water”.
Despite only a handful of people watching from the stands, Savsek’s victory was greeted enthusiastically by his team mates, with at least one jumping into the warm water to celebrate his near perfect run.
“It’s not so easy without spectators. We have just the Olympic Games where we can race in front of thousands of people,” said Rohan, whose father and coach Jiri Rohan won silver in the canoe slalom pairs in 1992 and 1996.
The pairs race was dropped from the Games in Rio to make way for women’s canoe slalom.
By Tim Kelly