After catching Chaves, Yates allowed the Colombian to take the stage win, even though it will cost him four bonus seconds which could prove expensive down the line.
After a gruelling final climb along a 150m stretch of road, Aru crossed the line - under the shadow of the Etna Astrophysical Observatory - with the main peloton, just 26 seconds behind race victor Johan Eseban Chavez (Mitchelton Scott).
Chaves knew that the toughest section of the climb began with a shade over five kilometres to go, and he waited for that precise point to unleash his winning attack, dancing past Giulio Ciccone (Bardiani-CSF) to solo clear.
Australian Rohan Dennis took a one second-advantage into the stage, but fell away in the final climb towards the top of Mt Etna.
With Chaves confidently ahead on his own, Yates bided his time amid a series of further skirmishes before pulling away in commanding fashion to join the Colombian in the final kilometre. "It's a dream for the team to have the stage, the pink jersey and the blue jersey". "I didn't really have to do anything, I could sit in the wheels and save energy". When Simon Yates caught me he said, come on, let's go, let's go, you take the stage today.
BC-CYC-Giro d'Italia, 133 Yates moves into overall lead of Giro, Chaves wins stage 6Eds: APNewsNow. "Hopefully that can help me in the next few stages", Yates explained.
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"I felt really good", Yates said afterwards.
It is a second stage win in the Giro for Chaves (after his success in 2016) - a remarkable achievement for the 28-year-old who was told he might never cycle again after a serious crash in 2013.
Chaves has moved up to third position and is 26 seconds back.
The Giro heads to the Italian mainland for Friday's seventh stage - a flat 159km route from Pizzo to Praia a Mare.
The Giro ends in Rome on May 27.