The Colombian continues a remarkable Vuelta for Australian team Orica, who now count three-stage wins after Caleb Ewan's victory on Wednesday and two stints in the leader's jersey, as Chaves finished five seconds ahead of Tom Dumoulin (Giant-Alpecin), who began Thursday's stage as race leader by one second.
The Dutchman could do nothing to counter Chaves' well-time attack 2.4km out on the steep slopes leading to the finish at Sierra Cazorla, quickly finding himself 15 seconds behind the 25-year-old on the category three climb.
Dumoulin attempted to bridge the gap on one of the flatter sections of the climb as he distanced the group of GC contenders behind. But he was unable to match the pace of the man out in front, and was eventually overtaken by the late attack of Dan Martin (Cannondale-Garmin), who took second place on the day with Dumoulin in third.
With the time bonuses he took as he sailed across the line to victory, Chaves now sits 10 seconds ahead of Dumoulin overall with another mountain stage tomorrow which will make the red jersey difficult to defend.
The 200.3km stage from Cordoba saw a six-man break finally get away after a fast start to proceedings in the 35 degree heat of southern Spain, with peloton averaging almost 50kmph in the first hour or racing.
Cyril Gautier (Europcar), Niki Terpstra (Etixx-Quick Step), Kristijan Durasek (Lampre-Merida), Peter Velits (BMC), Steve Cummings (MTN-Qhubeka) and Miguel Angel Rubiano (Colombia) were the men to set a gap out front, establishing over four minutes to the bunch behind before things began to tumble.
The cohesion between the six fell away as they approached the foot of the climb with 10k to go, and Britain's Cummings saw his opportunity to attack and attempt a solo effort to the finish.
The MTN man held off of the chasing group behind, which had now seen a huge number of riders dropped, for some time, but was eventually caught by Chaves on one of the steepest ramps with around 2km remaining and almost came to a stand still after his efforts during the day.
Chaves then went on to take his victory, as the GC hopefuls like Chris Froome (Team Sky), Alejandro Valverde (Movistar) and Nairo Quintana (Movistar) all finish together behind at 11 seconds back.
Friday's stage seven will likely see those rider reach out to establish time-gaps in earnest for the first time in the Vuelta, with a tought category one summit finish to La Alpujarra after a 191.1km route.
Vuelta a España stage six: Córdoba Sierra de Cazorla (200.3km)
1. Esteban Chaves (Col) Orica-Green-Edge, in 4-46-16
2. Daniel Martin (Irl) Cannondale-Garmin, at 5 secs
3. Tom Dumoulin (Ned) Giant-Alpecin, st
4. Ruben Plaza (Esp) Lampre-Merida, at 11 seconds
5. Alejandro Valverde (Esp) Movistar
6. Joaquim Rodriguez (Esp) Katusha
7. Chris Froome (GBr) Team Sky
8. Rafal Majka (Pol) Tinkoff-Saxo
9. Nairo Quintana (Col) Movistar
10. Nicolas Roche (Irl) Team Sky, all same time
Overall classification after stage six
1. Esteban Chaves (Col) Orica-Green-Edge, in 21-55-13
2. Tom Dumoulin (Ned) Giant-Alpecin, at 10s
3. Daniel Martin (Irl) Cannondale-Garmin, at 33s
4. Nicolas Roche (Irl) Team Sky, at 36s
5. Alejandro Valverde (Esp) Movistar, at 49s
6. Daniel Moreno (Esp) Katusha, at 51s
7. Chris Froome (GBr) Team Sky, at 55s
8. Joaquim Rodriguez (Esp) Katusha, at 56s
9. Nairo Quintana (Col) Movistar, at 57s
10. Fabio Aru (Ita) Astana, at 1-08
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