Alessandro De Marchi (BMC) and Dario Cataldo (Astana) looked set to contest a two-man sprint after breaking away from the leading group 15km from the finish but they were reined in within 50 metres of the line as Orica Scott's Impey surged ahead.
“It was an interesting day today with the splits,” Impey said. “We had quite a few guys in the front and in the end it was such a reduced front group.”
“I was just happy to have the legs for the sprint because I rode quite hard early on. We moved Yates up overall so to get the win on top of that is fantastic.
“Going into today’s stage I didn’t think I would have a good chance but the team rode so well.
“We knew it would be hard to drop the sprinters today but we had numbers in the front, Carlos Verona was doing strong turns so I am happy to finish it off with a win.”
Valverde (Movistar) took second ahead of 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 sitting at the rear of the peloton with his team-mates when the peloton split on the descent of Alt de Bot and they lost contact with the leading group. They gradually lost more ground, then hope, as the gap increased rapidly.
Valverde now leads Alberto Contador (Trek Segafredo) by 53 seconds and his Movistar team-mate Marc Soler, by one minute six seconds.
“It was another really tough day,” Valverde said. “The beginning of the stage was so fast, and it was all split down the first climb, which was even more difficult than the climbing itself.
“We always kept the front of the group and caught Froome unprepared behind, yet we only put Erviti out to work. There were so many teams interested on making that group stick, and the riders behind didn't have a chance to make up terrain.”
The seventh and final stage will take the peloton over 138.7km around Barcelona with Valverde likely to be confirmed as the overall winner.
“Now it's all down to Sunday,” Valverde said. “It shouldn't be a problem to keep the leader's jersey, yet we must race as focused as we've done over the week.
"There will surely be attacks and many riders are still pretty much together and up for the podium and top-ten fights.”