Roglič was the beneficiary of a lot of work from his Jumbo-Visma teammates throughout the stage, with the last remaining member of the breakaway, Mäder within sight as the gorup of favourites came into the final kilometres.
Roglič tried one surge that was thwarted by Schachmann, resting up as Lucas Hamilton (Team BikeExchange), Alexander Vlasov (Premier Tech-Astana) and Tiesj Benoot (Team DSM) rejoined before launching again with 500 metres remaining of the uphill run to the line.
This time, Roglič got the gap he needed, and with just enough time to overhaul Mäder 50 metres before the finish, a heartbreaking moment for the 24-year-old who would have claimed his first WorldTour win and who had worked hard from the breakaway for the entire stage.
Roglič took his third win of the 2021 edition of Paris-Nice, also strengthening his position at the top of the overall classification. The Slovenian superstar ended the day with an advantage of 52 seconds over Schachmann in second place, with Australians also moving up on the general classification with Hamilton moving up in sixth overall with his fourth placed finish and Jack Haig (Bahrain-Victorious) jumping into the top-10 with his performance.
"At the end, there was a possibility [to win the stage], and I went for it," he said. “It was hard all day, from the beginning. It was ‘short but sweet’, as we say. It was really really tight, but luckily I managed to come first over the finish line."
Earlier in the stage, it had been a fight to establish the breakaway as 13 riders broke clear on the category 2 ascent of Côte de Gilette. Among them green jersey wearer and two-time stage winner Sam Bennett (Dececuninck-QuickStep), along with Neilson Powless (EF Education-Nippo), Andrey Amador, Laurens De Plus (both Ineos Grenadiers), Alexey Lutsenko (Astana), Anthony Perez (Cofidis), Julien Bernard, Kenny Elissonde (both Trek-Segafredo), Thomas De Gendt (Lotto Soudal), David de la Cruz (UAE Team Emirates), Mattia Cattaneo (Deceuninck-Quick-Step), Dylan Teuns and Gino Mäder (both Bahrain Victorious).
With a number of riders close on the general classification to the lead of Roglič, Jumbo-Visma kept the break on a tight leash, not allowing them a lead over two and a half minutes at any point during the stage.
As the break began the climb, a 16-kilometre monster into the summit finish, their lead was just over a minute and the catch seemed inevitable.
The break began to splinter on the climb, with Bennett among those dropped and swallowed up by the bunch almost immediately. The group continued to drop through attrition, largely due to aggressive riding from Lutsenko, although the Kazakh himself was left behind by Elissonde, Powless and Mäder as they increased the pace.
Mäder then dropped his erstwhile companions with an attack with 7.5 kilometres remaining in the stage, going solo in a bid for his first WorldTour victory.
Behind, there had only been one brief attack from the peloton as Simon Geschke (Cofidis) tried his luck, but it was swallowed back up by Jumbo-Visma, with the other GC candidates no doubt fearing the same if they were to launch their own aggressions.
In the end, it was just a select group at the front after the Jumbo-Visma presence had been reduced to just the race leader and after a series of attacks, Roglič was able to pass Mäder and claim his third stage win of what has been a dominant Paris-Nice for the two-time Vuelta a Espana winner.