Damien Riat and Nino Niederreiter scored and Genoni made 28 saves for fifth-seeded Switzerland, which was six minutes away from getting to the semifinals of the Olympics for the first time. But then the lead and the win vanished.
"That's sports, I guess," Switzerland captain Roman Josi said. "We played a really good game, a really good first period.
"It's hard to explain right now. It's sports."
Switzerland jumped to a 2-0 lead with goals 1:12 apart in the first period.
The first came when Switzerland's Ken Jager intercepted a pass from Saros behind the net and fed it to Riat, who buried into the open goal to make it a 1-0 game at 14:14.
The Swiss made it 2-0 at 15:26 when Niederreiter, who had just jumped off the bench, took a pass from Pius Suter at the top of the left face-off circle and blasted a one-timer over the glove of Saros, who appeared to be screened by Finland defenseman Niko Mikkola.
Then Switzerland, with eight NHL players in its lineup, went into shutdown mode to smother a Finland team made up completely of NHL players.
Finland, however, never lost faith.
"I think everybody still believed in our team," forward Eetu Luostarinen said, "and that you can never, never give up. So even if there's a minute left and we're down two, you can still score two. We just have to believe."