Quintana sensed an opportunity when Konig swung off, but Froome stuck resolutely to his wheel in the wake of continued attacks as they passed Chaves.
Froome’s own acceleration helped stretch their advantage over the remaining chasers, and Quintana was left needing to dip deep just to hang on.
Another kick up the final ramp to the line brought victory for Froome, and ten bonus seconds, while Quintana took second and six bonus seconds.
Alejandro Valverde followed at six seconds, while stage six winner Simon Yates was also in the GC group, finishing sixth on the day to jump back up to seventh overall.
Froome was the man of the hour, however, with the Tour de France champion issuing a warning to Quintana that this race is far from over yet.
Vuelta a Espana: stage 11 – result
1) Chris Froome (GBR) – Team Sky – 3.44.47hrs
2) Nairo Quintana (COL) – Movistar – ST
3) Alejandro Valverde (ESP) – Movistar +6”
4) Leopold Konig (CZE) – Team Sky – ST
5) Alberto Contador (ESP) – Tinkoff
6) Simon Yates (GBR) – Orica-BikeExchange +13”
7) Michele Scarponi (ITA) – Astana +14”
8) Johan Esteban Chaves (COL) – Orica-BikeExchange +19”
9) Pierre LaTour (FRA) – Ag2r-La Mondiale +22”
10) Samuel Sanchez (ESP) – BMC Racing +30”
General classification
1) Nairo Quintana (COL) – Movistar – 42.21.48hrs
2) Chris Froome (GBR) – Team Sky +54”
3) Alejandro Valverde (ESP) – Movistar +1.05
4) Johan Esteban Chaves (COL) – Orica-BikeExchange +2.34
5) Alberto Contador (ESP) – Tinkoff +3.06
6) Leopold Konig (CZE) – Team Sky +3.09
7) Simon Yates (GBR) – Orica-BikeExchange +3.25
8) Michele Scarponi (ITA) – Astana +3.34
9) David de la Cruz (ESP) – Etixx-QuickStep +3.45
10) Samuel Sanchez (ESP) – BMC Racing +3.56