O'Connor came 12th in Thursday's stage, which ended with a climb up Mount Etna, and he lies 13th in the general classification (GC), one minute and 39 seconds behind Yates. Simon Yates (Mitchelton-Scott) 3.
Dutch rider Dumoulin is now second overall at 16sec behind Yates.
The two riders had broken from the leading pack at 10 kilometers from the finish. Keeping you up to date about what is happening in Colombia is costly and not without risk.
Yates attacked the other general classification hopefuls inside the final two kilometres, breaking away from the peloton and bridging to team-mate Chaves - the last survivor of the day's breakaway - and the pair crossed the line together, with Yates gifting the Colombian the stage win.
Coming out victorious was Esteban Chaves, though he was gifted the stage his ridiculously fast-finishing teammate Simon Yates, who moves into the leader's pink jersey while announcing himself as a serious contender for the overall title.
"It was wonderful to wear the pink jersey - something I was hoping for, but you never really expect it".
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Yates, 25, now leads a Grand Tour for the first time.
"I said to him (Chaves) as soon as I caught him that he could take the stage. I just had to get that wheel, and have a bit of patience as well".
Viviani had looked on course to take his third stage win of the race after taking the lead with the line in sight, but the Quick-Step Floors rider had to settle for second place on the same time.
"I just missed it, sadly, but it's certainly within reach later ... and really I'm so pleased to be up there with the best again on one of the most iconic climbs around and in the Giro d'Italia".
Chris Froome now trails Yates by 70 seconds on a day when he again looked below his best, although the four-time Tour de France victor did move up 11 places to eighth overall. When I was in his wheel, at 6 or 7 km to go, he was still looking good.