Froome finished in the peloton, 29 seconds after Yates, with race leader Darwin Atapuma (BMC Racing) and second-placed Alejandro Valverde (Movistar), meaning no change at the sharp end of the general classification.
Tour de France champion Froome is 32 seconds behind Atapuma, while Valverde sits second at 28 seconds.
Yates is 1’28” back and is now one of three Brits currently inside the top ten, with Peter Kennaugh – who wore the red jersey after Team Sky won the stage one team time trial – eighth at 1’14”.
Vuelta a Espana 2016: stage six – result
1) Simon Yates (GBR) – Orica-BikeExchange – 4.05.00
2) Luis Leon Sanchez (ESP) – Astana +20”
3) Fabio Felline (ITA) – Trek-Segafredo +22”
4) Ben Hermans (BEL) – BMC Racing – ST
5) Kenny Elissonde (FRA) – FDJ
6) Daniel Moreno (ESP) – Movistar
7) Mathias Frank (SUI) – IAM Cycling
8) Alejandro Valverde (ESP) – Movistar +29”
9) Romain Hardy (FRA) – Cofidis – ST
10) Simon Clarke (AUS) – Cannondale-Drapac
General classification
1) Darwin Atapuma (COL) – BMC Racing – 21.45.21hrs
2) Alejandro Valverde (ESP) – Movistar +28”
3) Chris Froome (GBR) – Team Sky +32”
4) Nairo Quintana (COL) – Movistar +38”
5) Johan Esteban Chaves (COL) – Orica-BikeExchange – ST
6) Samuel Sanchez (ESP) – BMC Racing +1.07
7) Leopold Konig (CZE) – Team Sky +1.12
8) Peter Kennaugh (GBR) – Team Sky +1.14
9) Gianluca Brambilla (ITA) – Etixx-QuickStep +1.22
10) Simon Yates (GBR) – Orica-BikeExchange +1.28