The wing scored twice in the first five minutes, before completing a ‘natural hat-trick’ (three consecutive goals) midway through the second period.
Ryan McDonagh added a fourth on a snap shot minutes later, while David Backes completed the early in the third period.
US goaltender Ryan Miller – who was named MVP at Vancouver 2010 – had just 17 shots to stop in the match, before letting his guard slip with 18 seconds left on the clock to hand the Slovenians a consolation goal.
“It's not about me it's about the win," said hat-trick hero Kessel. “We can still improve more and we have to get a lot better.”
Meanwhile, Ilya Kovalchuk overcame a mid-match injury to score in a penalty shootout and hand Russia a dramatic 1-0 victory over Slovakia.
It was the second consecutive shootout for the Russians who lost a heartbreaker 3-2 to the USA a day earlier. It also stirred memories of Vancouver 2010, when the Slovaks defeated Russia 2-1 in a shootout.
“Overall we played well,” said Russia’s Alex Ovechkin. “Everybody wants to beat Russia at home. It's the Olympic Games and nobody wants to make mistakes.”
Kovalchuk, who had gone off injured during the second period, came back to beat Slovakia goaltender Jan Laco with a backhand shot from close range.
Alexander Radulov also scored for Russia in the shootout, following a stand-out display, while Michal Handzus and Tomas Tatar failed on both their shootout attempts for Slovakia.
Russian captain Pavel Datsyuk believes his side still need to improve. “We're not happy about this game. We wanted to win it in regular time, not to go into shootouts or cause heart attacks,” he said.
The fact that they were unable to do so was in large part down to a superb display between the Slovakian posts from Laco, who racked up 36 saves.
Russia finished with two wins and a loss in Group A of the round robin and now advance to the qualification play-off round.
In Group B, Austria beat Norway 3-1 – their first win at an Olympic hockey tournament in 12 years - as star forward Michael Grabner continued his goal-scoring spree at Sochi 2014, with a double to take his total for the Games to five.
Grabner claimed an assist for the other goal, while Austrian goaltender Mathias Lange made 34 saves to keep the Norwegians at bay. That left the Scandinavians rock bottom of the group, with Austria finishing third.
Finland and Canada rounded off the day’s action, slugging out a battle for top spot in Group B at the Bolshoy Ice Dome.
Drew Doughty opened the scoring for the defending champions, sliding a snap shot under the leg of Finnish goaltender Tuuku Rask in the first period.
Tuomo Ruutu levelled for the Finns in the second, and the score stayed at 1-1, sending the game into overtime.
It took Doughty just 2.32 minutes to end the contest, providing another clinical finish to hand Canada top place in the group and an automatic berth in the quarter-finals, where they will be seeded third.
Finland join them in the last eight where they will be seeded fourth, having qualified as the strongest runners-up of the three groups, by virtue of a superior goal difference over Russia and Switzerland.
The other eight teams from the original 12 will now go into the play-off round to determine the other four quarter-finalists.
Qualification play-offs, 18 February:
Russia vs Norway
Switzerland vs Latvia
Czech Republic vs Slovakia
Slovenia vs Austria
Quarter-finals, 19 February
Sweden vs Slovenia/Austria
USA vs Czech Republic/Slovakia
Canada vs Switzerland/Latvia
Finland vs Russia/Norway