Welshman Geraint Thomas, of Sky, maintained his 1min 39sec race lead over teammate and compatriot Chris Froome after a 181.5km ride from Millau in which the yellow jersey holder’s rivals failed to launch a challenge.
Thomas and the main peloton trailed over the finish line just over 13 minutes in arrears on what, for them, was a comparatively easy stage ahead of Monday’s rest day.
Astana, meanwhile, took full advantage of what was set to be a transition stage ahead of three tough days in the Pyrenees mountains starting from Tuesday.
Nielsen was one two Astana riders who fought hard to get in a breakaway group of 29 riders, along with compatriot Michael Valgren.
And when it came to the final kilometres, the race debutant seized the day.
Nielsen first underlined his ambitions 8km from the finish when he quickly countered Italian Domenico Pozzovivo’s effort to break clear.
And two kilometres further on, Nielsen was quick to join Dutchman Bauke Mollema (Trek) and Jon Izagirre (Bahrain) when they left five of their breakaway companions behind.
A lack of cooperation in their wake meant the trio were allowed to build an insurmountable advantage over the closing kilometres.
But Nielsen was simply unbeatable after launching his sprint just under 300m from the finish, where Izagirre finished second and Mollema third.
It is Astana’s second consecutive win on the race after Spaniard Omar Fraile capped an audacious attack on the final climb of stage 14 to triumph in Mende.