The Americans bounced back from losses to Canada and Russia to win the finale of their round-robin schedule in the North American pool. They will be either the second or third seed in the quarterfinals, which begin next week.
Ladislav Nagy scored the lone goal for Slovakia, which fell to 0-2 in the tournament and will wrap up its preliminary round play on Sunday against Russia.
The Americans grabbed the lead just 3:09 into the game when Smolinski knocked in the rebound of a Brian Leetch shot.
Blake broke a 1-1 tie with a fluke goal. He led a rush into the Slovak zone and fed a pass to the right wing for Chris Chelios, who sent the puck back toward the slot. Blake was tripped up and slid toward the crease as the puck deflected off him and past Jan Lasak for the goal.
Earlier Friday, Vaclav Prospal had a goal and two assists to power the Czech Republic to a 7-2 rout of Germany in Prague.