Closer to the front, Groupama-FDJ's Thibaut Pinot is third, one minute and four seconds behind Yates, with Domenico Pozzovivo the highest-placed Italian rider in fourth spot.
Yates said: "Chaves just had a bad moment on the first climb of the day".
"He's getting better as the race goes on".
"The plan was that if it came back I would, of course, try".
Going into Tuesday's stage they were in the enviable position of occupying the top two positions in the overall standings, meaning tactically they would be able to play two cards in the pink jersey race and increase the pressure on their rivals.
Bennett sits two minutes and six seconds behind Yates.
"I'm very disappointed for him because he's worked hard for this Giro".
Race favourite Froome again lost steam in the final climb with the four-time Tour de France victor finishing in 42nd position, some 40 seconds behind Yates. I'm happy that I got more time on Tom.
British compatriot Chris Froome lost more seconds and the four-time Tour de France champion's chances of winning are all but over.
"The team is motivated and I'm motivated".
"I certainly haven't given up hope, " Froome said.
The hilly stage included a climb through Michele Scarponi's hometown of Filottrano in honor of the 2012 Giro victor who died after a collision with a van while training shortly before last year's race.
Three breakaway riders Alessandro De Marchi (BMC), Luis Leon Sanchez (Astana) and Fausto Masnada (Androni-Sidermec-Bottecchia) were caught five kilometres from the line before two steep climbs to the finish.
The Englishman, riding for Mitchelton-Scott, launched an opportunistic late attack in the run-in to the finish of stage 11 in the hilltop town of Osimo.