The 156 km (97 miles) stage started and finished in the French Riviera’s biggest city, but the unseasonable conditions with persistent rain saw a number of high-profile contenders hit the tarmac in bruising falls.
Kristoff was among the casualties but benefited from a “truce” called by leading riders in the peloton, which slowed dramatically for safety reasons, allowing victims of crashes to catch up and contest the finish.
It was only in the closing stages that racing began in earnest again, although a further mass crash just inside 3 km (2 miles) to go, left home favorite Thibaut Pinot among the casualties, the Frenchman getting up to finish the stage without serious injury.
UEA Team Emirates rider Kristoff used his experience in the finishing burst to take the honors from world champion Mads Pedersen of Denmark and Dutch rider Cees Bol. Seven-time green jersey winner Peter Sagan finished fifth in the dash for line.
For 33-year-old Kristoff, it was one of the highlights of his career and all the more remarkable having lost about six minutes in his crash.
“It’s a yellow jersey. I always dreamed about wearing it. Now it is a dream coming true. You cannot dream of a better start,” he told Eurosport.
Defending champion Egan Bernal of Colombia finished safely in the peloton, but one of his key Team Ineos support riders, Pavel Sivakov, came down twice.
Bernal’s compatriot, Astana captain Miguel Angel Lopez, suffered a particularly heavy tumble in a downhill slide that saw him slam face-first into a traffic sign.
One of the other race favorites, Primoz Roglic of Slovenia finished in the same time as Bernal, the Jumbo-Visma rider summing up the mood of the peloton on the first day of a three-week race.
“We all just wanted to not do stupid things. You can still have a race and a sprint, but it was not the intention of anyone to crash on the first day,” he told ITV 4.
Roglic, who has shown impressive form in the warmup races, will be expected to come more to the fore on Sunday’s 186 km (115 miles) stage, again starting and finishing in Nice, but featuring two major climbs to test the legs of the contenders for the overall classification.
The Tour was originally due to start in late June, but like most major sporting events was postponed because of the coronavirus pandemic.
It is being held with strict health protocols in place, with teams facing expulsion if two or more of their entire entourage, including riders and support staff, test positive for Covid-19.
Fans, who normally pack the roadsides, particularly on the major climbs, face heavy restrictions and only 100 spectators were allowed into the finishing area on the Promenade des Anglais on Saturday.
With Covid-19 infections increasing in France, there has been speculation that the Tour may not even reach its traditional finish in Paris, but French minister for sport and education Jean-Michel Blanquer gave an upbeat message.
“You can’t rule out the cancellation of the Tour, but it has been so well prepared that the possibilities of it happening are very weak,” Agence France-Presse quoted him at the start line Saturday.