The 26-year-old Spaniard, a team mate of the Tour de France champion for most of his professional career, broke in the last mountain of the day to finish on his own in Grenoble and take the laurels in a stage where the leaders had observed a ceasefire.
On the climb to the ski resort of Chamrousse, 30 kms from the finish, Navarro caught Italian Eros Capecchi and France's Thibault Pinot, who had both broken early on. The two were unable to take his wheel and finished second and third respectively, 34 seconds behind.
"Alberto had decided to take it easy today and I was given the go-ahead to attack on the last climb. I reached the top with a 50-second lead and I knew it would be enough," he told reporters.
Prologue winner Contador remained third overall, 1:41 behind Slovenia's Janez Brajkovic and 26 seconds behind American Tejay Van Garderen.
With a gruelling stage to l'Alpe d'Huez on Saturday, most contenders for final victory stayed out of trouble in the two big climbs of the day.
Navarro is aware he will have to work hard for the 2007 and 2009 Tour champion on the famous 21 turns leading to the top of l'Alpe d'Huez but he said he would still treat himself to a glass of champagne to celebrate.
"Man, this is my first pro victory," he said.
Navarro amply deserves the celebration as he was bold enough to chase behind a group who had gone almost from the gun in the Lautaret pass overlooking Serre-Chevalier, the starting point of the stage.
From 18 men at the start, the leading group was finally trimmed down to just Capecchi, Pinot and Spaniard Egoi Martinez when Navarro caught them.
The main pack reached Grenoble 3:04 behind Navarro, saving strength for Saturday's decisive 151.5-kms stage.
Stage five result
1. Daniel Navarro (Spain / Astana) 3hrs 26mins 15secs
2. Eros Capecchi (Italy / Footon) +34"
3. Thibaut Pinot (France / Francaise des Jeux)
4. Dimitri Champion (France / AG2R) +1:39"
5. Egoi Martinez (Spain / Euskaltel)
6. Christophe Moreau (France / Caisse d'Epargne)
7. Blel Kadri (France / AG2R) +2:40"
8. Pierre Rolland (France / Bbox - Bouygues)
9. Luis Pasamontes (Spain / Caisse d'Epargne)
10. Christophe Riblon (France / AG2R)
1. Janez Brajkovic (Slovenia/RadioShack) 19hrs 55mins 4secs
2. Tejay Van Garderen (U.S. / HTC - Columbia) +1:15"
3. Alberto Contador (Spain / Astana) +1:41"
4. David Millar (Britain / Garmin) +1:56"
5. Nicolas Vogondy (France / Bbox - Bouygues) +2:43"
6. Denis Menchov (Russia / Rabobank) +2:55"
7. Christophe Riblon (France / AG2R) +3:05"
8. Jurgen Van den Broeck (Belgium/Omega Pharma-Lotto) +3:06"
9. Christian Knees (Germany / Milram) +3:10"
10. Rein Taaramaee (Estonia / Cofidis) +3:28"