The pair finished together on top of the volcano in Sicily, after Chaves had attacked from the breakaway on the climb and Yates attacked from a group of overall favourites in the final 1.5km.
Yates, happy to take the six second bonus and second place to steal the overall lead from the dropped Rohan Dennis (BMC), let his Colombian team-mate roll across the line to take the day's victory having ridden in the break all day.
The main favourites, including defending champion Tom Dumoulin (Sunweb), Thibaut Pinot (Groupama-FDJ), Fabio Aru (UAE Team Emirates) and Chris Froome (Team Sky) all finished in an eight-man group 26 seconds back, with Pinot able to sprint ahead to take the final time bonus for third place.
Maglia rosa Dennis finished 1-04 back on the winner, and drops out of the overall lead as Dumoulin stays in second, 14 seconds behind Yates with Chaves in third place.
How it happened
A huge number of riders were desperate to make it into the early breakaway today, with racing going for over half an hour before a decisive group finally got away.
A group of 28 riders slipped out of the bunch with the GC teams finally slowing to allow them to drift off, however seemingly failed to realise the presence of Esteban Chaves, just 47 seconds down on GC and potentially aiming for a decent overall finish.
He was joined by team-mate Jack Haig, as well as Chad Haga and Sam Oomen (Sunweb), Alessandro De Marchi (BMC), Alessandro Tonelli and Giulio Ciccone (Bardiani-CSF), Mikaël Chérel, Quentin Jauregui and Nico Denz (Ag2r La Mondiale), David De La Cruz an Sergio Henao (Team Sky), Marco Frapporti and Francesco Gavazzi (Androni-Sidermec), Manuele Mori, Jan Polanc and Diego Ulissi (UAE Team Emirates), Edoardo Zardini (Wilier Triestina), Robert Gesink (LottoNL-Jumbo), Ben Hermans and Rubén Plaza (Israel Cycling Academy), Sebastian Reichenbach and Jérémy Roy (Groupama-FDJ), Niklas Eg (Trek-Segafredo) and Dayer Quintana (Movistar).
The group established a maximum gap of around 3-30, but it jumped between 2-40 to 3-10 as BMC chased on the front of the peloton behind in service of maglia rosa Rohan Dennis.
By 40km remaining, after a fast day of over 44kmh average speed, the break still had 2-30 with the finish to Mount Etna looming.
The gap gradually dropped towards the foot of the 16km categorised part of the climb, with the break carrying 1-24 onto the lower slopes with a number of riders immediately blowing up.
Robert Gesink was the first to attack out front with 14.4km to go and 1-12 on the bunch, with Chérel and Hermans following, but they were quickly caught before De Marchi tried his luck.
He was followed by Ben Hermans before Sergio Henao and Esteban Chaves attacked with 11.8km to go. They again, were eventually forced to slow and reform in the group.
Ciccone then attacked with 9.8km to go but was reeled in, before trying again with 6km to go as the reduced group of five riders chased behind with around 40 seconds on the bunch.
Chaves then pushed on with 5.3km to go and was able to shake Henao, who had been marking him, riding straight past Ciccone, gaining around 35 seconds on the main bunch and 23 on his breakaway rivals.
Tom Dumoulin (Sunweb) pushed on with number of favourites from the main group, with Froome put into immediate trouble along with maglia rosa Rohan Dennis.
Froome was able to work his way back in as the favourites caught everyone but Chaves, but Dennis continued to struggle with 3.3km to go.
Pozzovivo dragged out a group of Bennett, Yates, Pinot with 3km to go as Dumoulin chased and brought them back with Chaves still 20 seconds up the road.
Those movements from the favourites' group seemed to put them at somewhat of a stalemate heading into the final 1.5km, with Simon Yates attacking with 1.4km to go after seeing his rivals just watching each other.
The Briton quickly caught Chaves within the last kilometre, and the pair rode together towards the finish line where Chaves was allowed to roll across the line alongside his team-mate to take victory, with Yates moving into the overall lead.
Pinot was able to sprint from the group of favourites behind for third place and the four bonus seconds, with Froome finishing at the back of the group. Dennis finished 1-04 down on the winner, but remains in the top-10 overall.
Friday's stage will see the riders head to Italy's mainland for a flat 159km sprinters' stage from Pizzo to Praia a Mare, with two mountain stages to come at the weekend.
Giro d'Italia 2018, stage six: Caltanissetta to Etna (164km)
1 Esteban Chaves (Col) Mitchelton-Scott, in 4-16-10
2 Simon Yates (GBr) Mitchelton-Scott
3 Thibaut Pinot (Fra) Groupama-FDJ, at 26s
4 George Bennett (NZl) LottoNL-Jumbo
5 Domenico Pozzovivo (Ita) Bahrain-Merida
6 Miguel Angel Lopez (Col) Astana Pro Team
7 Richard Carapaz (Ecu) Movistar Team
8 Tom Dumoulin (Ned) Team Sunweb
9 Fabio Aru (Ita) UAE Team Emirates
10 Chris Froome (GBr) Team Sky, all same time
General classification after stage six
1 Simon Yates (GBr) Mitchelton-Scott, in 22-46-03
2 Tom Dumoulin (Ned) Team Sunweb, at 16s
3 Esteban Chaves (Col) Mitchelton-Scott, at 26s
4 Domenico Pozzovivo (Ita) Bahrain-Merida, at 43s
5 Thibaut Pinot (Fra) Groupama-FDJ, at 45s
6 Rohan Dennis (Aus) BMC Racing Team, at 53s
7 Pello Bilbao (Esp) Astana Pro Team, at 1-03
8 Chris Froome (GBr) Team Sky, at 1-10
9 George Bennett (NZl) LottoNL-Jumbo, at 1-11
10 Fabio Aru (Ita) UAE Team Emirates, at 1-12
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