It’s Nielsen’s second stage win after winning a bunch gallop on stage 18, beating Daniele Bennati (Tinkoff) and Gianni Meersman (Etixx-Quick Step) to the line on stage 21.
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Quintana rolled across the final finishing line in the main peloton, securing his 1-23 victory over second placed Chris Froome (Team Sky), with fellow Colombian Esteban Chaves (Orica-BikeExchange) claiming third place narrowly ahead of three-time winner Alberto Contador (Tinkoff).
For all the top three, it represents their second finish on a Grand Tour podium in 2016, with Froome winning the Tour de France as Quintana came third, and Chaves taking second place at the Giro d’Italia.
The final stage to Madrid began in usual Grand Tour tradition; champagne and photos for the race leader and classification winners.
It took until almost halfway through the 104.8km stage, on arrival in Madrid, for the race to really begin, and four men eventually settled on a breakaway with Peter Kennaugh (Team Sky), Quentin Jauregui (Ag2r – La Mondiale) and Loïc Chetout (Cofidis), Koen Bouwman (Lotto NL Jumbo) going up the road.
But they never really established anything more than a minute and the peloton were able to keep them at a comfortable distance as they took the circuits in the Spanish capital.
One by one the breakaway riders were reeled in, with Chetout the last to hang on until just over 5km to go.
It was then down to the sprinters teams to line-up their fast men for the final victory, with Giant-Alpecin doing a lot of work to set up Nikias Arndt.
Etixx also fought hard to put two-time stage winner Meersman in the right position, but it was Bennati who hit out first. Meersman then looked to be coming in strong but Nielsen was able to come between them to score the victory.
But the day will belong to Quintana, who adds the Vuelta win to his 2014 Giro d’Italia victory ahead of his big rival Froome.
Vuelta a España stage 21, Las Rozas – Madrid (104.8km)
1. Magnus Cort Nielsen (Den) Orica-BikeExchange, in 2-48-52
2. Daniele Bennati (Ita) Tinkoff
3. Gianni Meersman (Bel) Etixx-Quick Step
4. Kristan Sbaragli (Ita) Dimension Data
5. Nikias Arndt (Ger) Giant-Alpecin
6. Lorenzo Manzin (Fra) FDJ
7. Romain Hardy (Fra) Cofidis
8. Jhonatan Restrepo (Col) Katusha
9. Rudiger Selig (Ger) Bora-Argon 18
10. Salvatore Puccio (Ita) Team Sky, all same time
Final General Classification
1. Nairo Quintana (Col) Movistar in 83-31-28
2. Chris Froome (GBr) Team Sky at 1-23
3. Esteban Chaves (Col) Orica-BikeExchange at 4-08
4. Alberto Contador (Esp) Tinkoff at 4-21
5. Andrew Talasky (USA) Cannondale-Drapac at 7-43
6. Simon Yates (GBr) Orica-BikeExchange at 8-33
7. David de la Cruz (Esp) Etixx-QuickStep at 11-18
8. Daniel Moreno (Esp) Movistar at 13-04
9. Davide Formolo (Ita) Cannondale-Drapac at 13-17
10. George Bennett (NZl) LottoNL-Jumbo, at 14-07
Points classification: Fabio Felline (Ita) Trek-Segafredo
KOM classification: Omar Fraile (Esp) Dimension Data
Combination classification: Nairo Quintana (Col) Movistar
Team classification: BMC Racing (USA)