Froome finished with 2017 Giro champion Tom Dumoulin (Sunweb) and his other rivals despite being gapped at certain points on the 16-kilometre volcanic climb.
"I was happy just to be in the main group of favourites with Tom Dumoulin and the other guys," Froome said.
"My objective is to build through this race and be at my best in the third week, and I'm still on track for that."
In the 28-man move, which had Chaves, Sky counted David de la Cruz and Sergio Henao. They dropped back to support Froome on the final climb.
"The team did a good job, we were up front and also represented in the breakaway with Sergio Henao and the guys did a good job positioning me into the final to keep me safe and up there, ready for the climb," Froome added.
"So I think all in all, I'm just happy to tick this day off and looking forward to reaching mainland Italy and carrying on with the Giro.
"I think it was a really well executed stage by Mitchelton-Scott with Chaves in the break today it put a lot of pressure on the other GC contenders to work behind, BMC especially, so congratulations to them for taking the stage win and the pink jersey today."
Sports director Dario Cioni waited for Froome at the anti-doping check after the stage. Afterwards, he was due to fly with Fabio Aru and other favourites via helicopter to Italy's mainland in the Reggio Calabria region.
"How is Chris? It was the first summit finish, so it was a question mark, but we knew he was there in the Tour of the Alps with [Domenico] Pozzovivo and [Thibaut] Pinot. We were faithful. We know that he's growing and improving, so it's fine," Cioni said.
"If he was feeling well and had a chance to attack, but the chance wasn't there. He knows how to manage it, he knows where the finish line is, so he managed it at his own pace then to follow every attack."
The next summit finish is Montevirgine on Saturday. With Yates in charge, Froome sits in eighth overall at 1-10 minutes back with the time loses from day one and four calculated in.
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