Sagan was mobbed by fans as he crossed the line in 6 hours 28 seconds and admitted that, after leaving it so late, he feared the hattrick was in jeopardy.
"For the last five kilometers, I said to myself, it’s already done. But it’s unbelievable. This is something special. You saw in the climb, we were in pieces. And at the finish, it all happened in seconds. I am very happy, thank you to all my national teammates."
Sagan, who was disqualified from this year's Tour de France, merged out of the final corner in the perfect position on Kristoff's shoulder and just had enough to edge past the Norwegian, as Australia's Michael Matthews took third.
After his win, Sagan dedicated his victory to Italian Michele Scarponi, who died in April following a crash with a van near his home in Italy.
"I want to dedicate this third world title first to Michele Scarponi because he has his birthday tomorrow [Monday]. I'm very sorry this year, I want to wish luck to his family.
"And secondly I want to dedicate this victory to my wife, she's expecting a baby. It's a very nice finish to this season, I'm very happy."
Sagan joins a select band of riders who have been world champion three times but is the only man to do it in consecutive years.
mp /dv (AFP,Reuters)