Italians Alessandro De Marchi and Dario Cataldo looked set to contest a two-man sprint after jumping away from the leading group 15km from the end but they were reined in within 50 metres of the line as Orica Scott's Impey surged ahead.
Spain's Alejandro Valverde (Movistar) took second place ahead of French champion Arthur Vichot (FDJ) to extend his overall lead while Team Sky's Froome, who started the day in second place, lost more than 20 minutes.
The Tour de France champion was far back in the pack with all his team mates when it split in a descent and the whole Team Sky lost contact with the leading group.
They gradually lost ground, then hope, as the gap increased rapidly.
Valverde now leads his compatriot Alberto Contador (Trek Segafredo) by 53 seconds and another Spaniard, his Movistar team mate Marc Soler, by one minute six seconds.
Sunday's seventh and final stage will take the peloton over 138.7km around Barcelona.
(Writing by Julien Pretot; Editing by Clare Fallon)
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