The gold-medal match is scheduled for Saturday at 11:10 p.m. ET.
Koshechkin is 3-1-0 after getting the nod to start over NHL prospects Ilya Sorokin and Igor Shestyorkin and will almost certainly start in the final.
It's the Russians' first trip to the gold-medal game since 1998. The Czech Republic has a chance for its first bronze medal since 2006.
Kontinental Hockey League star Nikita Gusev and Vladislav Gavrikov scored goals 27 seconds apart in the second period on plays Czech goaltender Pavel Francouz had little chance of stopping. Kirill Kaprizov jumped in to screen Francouz on Gusev's goal that was upheld after a goaltender interference challenge, and Gavrikov put the puck into an empty net on a 2-on-1 rush with Ivan Telegin.
Ilya Kovalchuk added an empty-netter with 20.9 seconds left to seal the win. "We came here for one reason," Kovalchuk said. "We deserve to be in the final."
In scoring twice on 19 shots against Francouz, the favoured OAR were not overly powerful but certainly as opportunistic as they were in a 4-0 victory over the United States in group play. Former NHL superstar Kovalchuk made more of an impact with a questionable hit that injured Czech forward Jan Kovar than with any kind of offensive production until the empty-netter.
In a tournament without NHL players, the OAR brought a roster almost entirely made up of players from SKA St. Petersburg and CSKA Moscow, the top two teams in the KHL. That includes Kaprizov, a Minnesota Wild prospect who has been one of the best players in the tournament and could be in the NHL as soon as next season.
Second and third goalies Sorokin and Shestyorkin could be there soon, too, but they're definitely lower on the depth chart than Koshechkin, who has earned the right to be the OAR's No. 1 as one of the rare players not from SKA or CSKA.