Movistar's Valverde, 32, crossed the finishing line in Eibar just centimetres ahead of fellow Spaniard Joaquin Rodriguez after a 155-kilometre ride from the vineyards of Faustino V in Oyon.
In the race's first real work-out for the climbers, Briton Christopher Froome, runner-up in the Tour de France, took third place just ahead of Spaniard Alberto Contador, back from a hotly contested doping ban.
Saxobank's Contador, racing before his home crowd, needs a victory to turn the page on a two-year back-dated doping ban imposed on February 6 after he tested positive for traces of the banned substance clenbuterol.
Contador has not swayed from his defence that his positive test was caused by a contaminated steak he ate on the eve of the test.
But the 29-year-old two-time Tour de France winner (he was stripped of the third win in 2010, along with his Tour of Italy title of 2011) faces severe competition here, not only from Froome but also from Dutchman Bauke Mollema, with Rabobank, and the new leader, Valverde.
The third stage, which presented riders with four ascents including a category 1 climb to Arrate just ahead of the finish, began with a breakaway group that quickly grew to eight riders.
The leaders, including Belgian Philippe Gilbert (BMC), managed to put more than four minutes between themselves and the peloton at one point, with the temperature hitting 38 degrees Celsius in the mid-afternoon.
But their lead was whittled down to just seconds some 10km from the finish, and then the fight began in earnest.
Contador made repeated attacks on the lead in the final kilometres but failed to squeeze out Valverde, who snatched the red jersey from compatriot and Movistar team-mate Jonathan Castroviejo.
Dutchman Pim Ligthart of Team Vacansoleil-DCM won the 'King of the Mountains' polka dot jersey as best climber of the stage.
On Tuesday, the Vuelta's riders face a spectacular 160km fourth stage from Barakaldo in the Basque Country to Valdezcaray in Rijoa, near a popular ski resort.
Result of the third stage of the Tour of Spain, a 155.3km ride from Oyon to Eibar on Monday (leading riders only):
1. Alejandro Valverde (ESP) 3hr 49min 37sec, 2. Joaquin Rodriguez (ESP) same time, 3. Chris Froome (GBR) s.t., 4. Alberto Contador (ESP) s.t., 5. Daniel Moreno (ESP) at 0:06sec, 6. Bauke Mollema (NED) 0:06, 7. Eros Capecchi (ITA) 0:06, 8. Benat Intxausti (ESP) 0:06, 9. Andrew Talansky (USA) 0:06, 10. Robert Gesink (NED) 0:06
Selected:
22. Juan Jose Cobo Acebo (ESP) 0:50
Overall standings:
1. Alejandro Valverde (ESP) 8hr 46 min 56sec, 2. Benat Intxausti (ESP) at 18sec, 3. Joaquin Rodriguez (ESP) 19, 4. Christopher Froome (GBR) 20, 5. Alberto Contador (ESP) 24, 6. Bauke Mollema (NED) 28, 7. Robert Gesink (NED) 28, 8. Rigoberto Uran (COL) 30, 9. Daniel Moreno Fernandez (ESP) 33, 10. Igor Anton (ESP) 46, 11. Nicolas Roche (EIR) 52, 12. Eros Capecchi (ITA) 59, 13. Juan Jose Cobo (ESP) 1min 06sec, 14. Sergio Luis Henao Montoya (COL) 1:11, 15. Winner Anacona Gomez (COL) 1:12