The 21-year-old, riding his second Grand Tour, started the day in 19th place overall but propelled himself into 9th with an impressive ride on the first summit finish of the race.
He finished 9th on the stage, 3:34 down on winner Ilnur Zakarin (Katusha-Alpecin) but 37 seconds down on Primoz Roglic (Jumbo-Visma) and Vincenzo Nibali (Bahrain-Merida), the two race favourites who marked each other on the Colle de Nivolet.
With just under three kilometres to go, Sivakov had ridden away from the pair as Rafal Majka (Bora-Hansgrohe) and Richard Carapaz (Movistar) attacked from the elite group, but he was brought back.
"I didn’t really attack them [Roglic and Nibali] because they were looking at each other. I took one opportunity to go away because I knew I just had to ride my own pace," Sivakov said.
"I rode that final climb like a time trial. At the end I didn’t really look at then when they came back. I just kept doing my own thing in my own bubble."
In any case, Sivakov finished ahead of the likes of Simon Yates (Mitchelton-Scott) and Miguel Angel Lopez (Astana). With Lopez, that was crucial in moving into the white jersey for best young rider, which was taken from Hugh Carthy (EF Education First), who finished nearly seven minutes down on Sivakov.
Sivakov now leads that classification from Lopez at 35 seconds, with Valentin Madouas (Groupama-FDJ) the next best at 4:11. Lopez finished 11th on the stage but was held back by an untimely mechanical problem, and, a podium finisher at the Giro last year, will be a tough nut to crack.
"It's great. I really didn't expect to take this jersey today. But yeah, I was with Nibali and Roglic and all the top guys in the finale. It really was exceptional," Sivakov said.
"For sure this is going to be an objective - I'll try to keep this white jersey. It will be difficult, especially with Lopez there who had some bad luck in the finale today. I think it will be tough to compete with him as he’s not just fighting for the white jersey he’s fighting for the Giro and it’s far from over. It’s going to be a battle but I’ll do my best."