The 153.4km stage ended with a select group battling out on the mountain finish to San Miguel de Aralar, with Aru triumphing.
The 24 year-old Sardinian, who was third in the Giro earlier this year, moved up to seventh in the overall standings in the season's last Grand Tour on the back of the stage win, albeit still 2min 13sec behind leader Alberto Contador (Tinkoff-Saxo).
The Spaniard finished with Alejandro Valverde (Movistar), Joaquim Rodriguez (Katusha) and Sky's Chris Froome to see the stage end with no major changes in the overall classification.
However, Contador's hopes of winning his third Vuelta title were boosted, as Movistar's Nairo Quintana saw his campaign end in dramatic fashion. The Colombian broke a bone in his right shoulder early in the stage, in what was his second crash in as many days. The injury is expected to end his season.
A tough end to a Vuelta that had begun with so much promise for the Colombian, he will undergo an operation, Thursday.
For Aru though there were only tears of joy at the end of the gruelling stage.
"It's unbelievable," said Aru. "I am very pleased. It is fabulous for me and for the team who have all worked so hard to get this to happen.
"I don't think it is feasible for me to win the overall title, but I hope I can repeat this stage victory."
Contador, who took over the lead after Tuesday's time trial came in fourth in the stage itself just ahead of Britain's 2013 Tour de France winner Chris Froome.
The Spaniard holds a 20sec lead over compatriot Alejandro Valverde, who was second on the stage, while Froome is in fourth, 1min 21sec in arrears.
"I have many potential rivals still in the hunt so I have to look after my race and not try and sit back and watch what they are doing," said the 31 year old.
"It is going to be difficult for me to stay in the lead till the end but I feel good and my performance in the time-trial on Tuesday was a real confidence booster," he added.
Contador, who himself failed to finish the Tour de France after he broke his tibia in the early stages, said he felt sorry for Quintana.
"It's really a pity for the race. It is been a really crazy year. It happened to Purito (Rodriguez) in the Giro, then to Froome and me in the Tour and now to Nairo. This sport is like that and we have to make hay when the sun shines," he said.
"I am sad for Quintana because he really prepared hard for this race," added Contador.
Thursday's 12th stage will come as a relief to the sprinters, who have had a tough past couple of days first with the time-trial and then with this tough mountain stage, as it is a flat picturesque 166.4km ride amongst the vineyards beginning and finishing in Logrono, the winemaking centre of Spain.
SBS will broadcast eight live stages of the Vuelta a Espana, in addition to daily highlights.
Stage 11: 153.4km, Pamplona
1 Fabio Aru (ITA) Astana Pro Team 3hr 41min 03sec
2 Alejandro Valverde Belmonte (ESP) Movistar Team 0:00:06
3 Joaquin Rodriguez Oliver (ESP) Team Katusha
4 Alberto Contador Velasco (ESP) Tinkoff-Saxo
5 Christopher Froome (GBR) Team Sky
6 Rigoberto Uran Uran (COL) Omega Pharma - Quick-Step Cycling Team 0:00:13
7 Samuel Sanchez (ESP) BMC Racing Team 0:00:15
8 Daniel Martin (IRL) Garmin Sharp
9 Daniel Navarro Garcia (ESP) Cofidis, Solutions Credits 0:00:16
10 Robert Gesink (NED) Belkin Pro Cycling Team 0:00:21
1 Alberto Contador Velasco (ESP) Tinkoff-Saxo 40hr 26min 56sec
2 Alejandro Valverde Belmonte (ESP) Movistar Team 0:00:20
3 Rigoberto Uran Uran (COL) Omega Pharma - Quick-Step 0:01:08
4 Christopher Froome (GBR) Team Sky 0:01:20
5 Joaquin Rodriguez Oliver (ESP) Team Katusha 0:01:35
6 Samuel Sanchez (ESP) BMC 0:01:52
7 Fabio Aru (ITA) Astana 0:02:13
8 Winner Anacona Gomez (COL) Lampre-Merida 0:02:22
9 Robert Gesink (NED) Belkin Pro Cycling Team 0:02:55
10 Damiano Caruso (ITA) Cannondale 0:03:51