Kessel scored after 63 seconds to give the 2010 silver medallists a 1-0 advantage, then scored twice more without interruption to build the Americans' lead to 3-0.
The win concluded the three-game preliminary round for the undefeated United States, who advance to the quarter-finals by virtue of winning Group A.
Slovenia, who spoiled netminder Ryan Miller's shutout bid with 18 seconds left, will play a qualification game on Tuesday against an as-yet undetermined opponent with a berth in the quarter-finals on the line.
Meanwhile Russia battled to a 1-0 shootout win over stubborn Slovakia to close out preliminary round play in the Olympic men's ice hockey tournament but will have to wait to see if it was enough for a bye into the quarter-finals.
With a three periods and overtime unable to produce a result, Russia faced a shootout for the second consecutive day.
Ilya Kovalchuk and Alexander Radulov scored past brave Slovakian netminder Jan Laco to give the host nation a heart-stopping win and a chance to go directly through to the last eight.
With the United States (3-0) securing top spot in Group A, Russia will finish runners-up and will now have to rely on having the best second place record to secure the free pass.
Russia have made tough work of the preliminary round, scrapping to a win over minnows Slovenia in their opener followed by an epic eight-round shootout loss to the United States on Saturday and a shootout victory over winless Slovakia.
"Overall we've played well. Everybody wants to beat Russia at home," said Russian forward Alex Ovechkin. "It's the Olympic Games; nobody wants to make mistakes.
"We take what we take, and we're going to play in the future."
With the distraction of the 'Miracle on Ice' rematch with the United States behind them, the Russians came out focused on the business of getting to the final which will be decided next Sunday, the final medal of the Games.
While another raucous flag-waving crowd filled the Bolshoy Ice Dome, the atmosphere could not match the electricity that had crackled through the futuristic arena 24-hours earlier when Russia lost 3-2 in breathtaking shootout to the Americans.
Having lost to Slovakia in two of their previous three Olympic meetings, Sunday's clash was not one Russians could take lightly.
The Slovakians came ready for a fight outshooting Russia 22-16 through the opening two scoreless periods in a contest that had turned into a classic goaltending duel between Laco and Russia's Semyon Varlamov.
Both netminders opened the final period with dazzling saves but it was the Russian dialing up the pressure outshooting Slovakia 15-2, twice watching the puck clang off the post.
"When it hits the post, it's not goal," said Laco. "We did not win and you play the games to win. It was a good game but we were still unsuccessful.
"We have been well prepared for the game and I think we played very well even though the last period was really hard."
Laco continued to frustrate Russia's explosive forwards in overtime but the host nation quickly ended the suspense in the shootout, Varlamov stopping Tomas Tartar and Michal Handzus while Kovalchuk and Radulov finally put pucks behind Laco.
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