The Sky rider's rear wheel lost grip on a hairpin turn following a storm before the final climb 5.5km from the line to further dent the confidence of 32-year-old in a race he hasn't competed in since 2010.
Four-time Tour de France victor Froome had been ninth - 1 minute, 10 seconds behind Yates.
Simon Yates continues to make an extraordinary impact on the Giro d'Italia.
"Since the beginning of the day we believed in the possibility of winning the stage as well as defending the Maglia Rosa".
Attacks started from the break and Fausto Masnada got away before he too was reeled in 2.7K from the line, setting up the final attack and victory for Yates.
"I realise how big it is to win my first stage with the pink jersey", said Yates, who became the first Briton since Mark Cavendish in 2013 to win a stage and only the second after Robert Millar in 1987 on the top of a mountain. Despite help from a teammate it was clear that there would be some serious damage done to his position on GC.
Italy's Davide Formolo (Bora) finished second followed by France's Thibaut Pinot (FDJ), who crossed in third to move up in the overall standings to fourth, 41sec behind Yates. "However, it's still a good day for us, I think". We have two more weeks coming up and hopefully we have some better days, " Team Sky coach Nicolas Portal said.
Fourteen riders rode off the front as the flag dropped for the 225km stage and with Gianluca Brambilla (Trek Segafredo) the closest threat on the general classification at six-minutes 40seconds down, the peloton was content to let them extend their lead to several minutes.
Tomorrow the Giro-2018 second rest day, and on Tuesday the participants of the race will overcome the 239-km stage with three category nodes.