The Americans finished first in Group A and thus earned some rest until Wednesday, when the four quarterfinals will be played.
Canada and Russia, meanwhile, both won overtime games Sunday to create the final pairings for the rest of the tournament.
Kessel, who plays his NHL hockey for the Toronto Maple Leafs, scored his team's first three goals. The opening score came just 1:04 into the contest. Kessel put in an easy rebound midway through the second period to give the Americans a 3-0 lead.
Miller did not allow a goal until there were 18 seconds left to play.
The United States was able to recover from the emotional strain of the thrilling game it played 24 hours earlier, which turned out to be a classic 3-2 shootout victory over the Russians.
Russia, however, struggled to bounce back and did not score a goal in regulation or overtime against a Slovakian squad that had lost its previous two games by a combined 10-2 margin.
Saturday's shootout against the Americans lasted eight rounds, but the one against Slovakia on Sunday went just two. Alexander Radulov and Ilya Kovalchuk both scored and Russian goaltender Semyon Varlamov stopped both the Slovak attempts.
Canada then found itself in a 1-1 tie with Finland after regulation play, but the Canadians emerged with a 2-1 victory when Drew Doughty scored 2:32 into the extra period.
The three group winners plus the next best point earlier in group action advanced to the quarterfinals. The other eight teams in the Olympic tournament have been paired for games on Tuesday to determine which will move on to the quarters.
By virtue of piling up nine points with its three victories in Group C, Sweden emerged as the No. 1 seed heading into the knockout portion of the Olympics. The United States and Canada both had eight points, having to settle for two points for their wins in overtime, but the Americans had a better goal differential than did Canada and thus earned the No. 2 seed.
Canada wound up third and Finland had the best record among those who did not win a group.
Tuesday's qualification games will send Russia against Norway, Switzerland against Latvia, the Czech Republic against Slovakia and Slovenia against Austria.
Sweden will take on the Slovenia-Austria winner in the quarterfinals, the United States will face the Czech Republic-Slovakia winner, Canada will play the Switzerland-Latvia winner and Finland will meet the Russia-Norway winner.