Van der Poel cut an emotional figure after winning the stage atop the Mur de Bretagne, having achieved a feat his late grandfather, Raymond Poulidor, famously failed to accomplish during his own career.
Despite launching an attack on the first ascent, the Alpecin-Fenix rider made one final push to power past the rest of the field and cross the line six seconds ahead of Tadej Pogacar (UAE Team Emirates) and Primoz Roglic (Jumbo-Visma), who finished second and third respectively.
With two days in the flatlands ahead, van der Poel could yet keep a hold of the yellow jersey and now leaves the rest of the general classification contenders with plenty of work to do.
Team Ineos-Grenadiers are among those in need of instant improvement after Geraint Thomas finished 23 seconds behind his Dutch rival.
Thomas’ form is of particular concern at this point, particularly after teammates Richie Porte and Tao Geoghegan Hart both lost time due to two opening day crashes.
As for Wilco Kelderman, however, the 30-year-old’s fourth-placed finish ahead of stage one-winner Julian Alaphilippe (Deceuninck Quick-Step) was a positive for Bora-Hansgrohe, while Australian Jack Haig (Team Bahrain Victorious) rounded out the top 10, two seconds adrift.
Mathieu van der Poel (Alpecin-Fenix), 1st overall
“I have no words…” said van der Poel, stopping for some time before being able to answer.
“You can’t even plan something like this. I launched my first attack here with one to go, I kept going until I had those bonus seconds, my only and my last chance at this Tour to grab the yellow jersey. To finish it off like this, it’s incredible.
“The last 500 metres was really painful but I knew I had to keep on going just to get the gap. It wasn’t until five minutes after that I knew I had the yellow jersey."
Tadej Pogacar (UAE Team Emirates), 3rd overall, 13 seconds behind
"The day started well, as all my teammates involved in yesterday’s crashes managed to start, including Marc Hirschi," Pogacar told the team's website.
"I would have liked to fight to win, but it was also nice to see van der Poel win, today he was the best and he also surprised everyone by attacking already on the first pass on the Mur.
"He also asked me, jokingly, if I wanted to attack with him the first time up.”
Jack Haig (Team Bahrain Victorious), 6th overall, 26 seconds behind
"I think you can see through the year that I've slowly improved each time trial and I was happy with my performance in the one at the Criterium du Dauphine," Haig told SBS Cycling Central ahead of the upcoming time trials.
"The team's invested more into research and development there because the technology side of the sport is becoming more important, especially in time-trialling and you see that with the top teams."
Geraint Thomas (Team Ineos-Grenadiers), 20th overall, 41 seconds behind
"The stage was complicated... It’s a bit of a shame that G lost a few seconds but we remain in the fight and there is a lot to come," said 18th-ranked teammate, Richard Carapaz.
Lucas Hamilton (Team BikeExchange), 25th overall, 1’16 behind
"It got pretty heavy on the final circuit there and most of the type of riders like (Michael) Matthews got isolated at the finish," Team BikeExchange head sport director Matt White said.
"We’ve lost our place on GC but Esteban (Chaves) and Lucas Hamilton were up there in the front part of the group at the finish."
Miguel Angel Lopez (Movistar Team), 33rd overall, 2’22 behind
"It was such a hard stage, one of attrition, just like everyday on week one of the Tour de France," said 11th-ranked teammate, Enric Mas.
"When it comes to the team, I think we didn’t suffer any setbacks, so on that side it was a fine day."
Richie Porte (Team Ineos-Grenadiers), 43rd overall, 3’08 behind
"The pull by Richie Porte was incredible to put us into a good position... we will see little by little, day by day," Carapaz told the Ineos website.
The Tour de France continues tonight with Stage 3; one for pure sprinters like Aussie Caleb Ewan. Watch on SBS, the SKODA Tour Tracker App and SBS On Demand from 8.30pm (AEST), with live racing commencing at 9:00pm.