The Americans found themselves in a 1-1 game early in the second period before unleashing a barrage that produced six goals in the middle stanza.
On a busy day of Olympic hockey, Finland defeated Austria 8-4, Russia had a tougher time than expected with Slovenia before emerging with a 5-2 victory and defending champion Canada fought off Norway 3-1.
Kesler, who plays for the Vancouver Canucks, put the Americans in front to stay just 62 seconds after Tomas Tatar had lifted Slovakia into a tie.
The United States produced four of its second-period goals in a span of 12:04, driving Jaroslav Halak of the St. Louis Blues out of the Slovakia net. Peter Budaj of the Montreal Canadians replaced him and promptly gave up two goals over the course of just 57 seconds.
Russia held a 3-2 lead over Slovenia before Valeri Nichushkin and Anton Belov delivered goals 3:54 apart in the third period.
The Americans, along with Russia, Slovenia and Slovakia, make up Group A in the men's tournament. A regulation win gives a team three points, an overtime win is worth two points and an overtime loss nets one point.
The three group winners and the next best team all reach the quarterfinals. The other eight teams in the tournament will then battle for the other four quarterfinal spots.
Finland had to come from behind twice against Austria in their Group B opener. Olli Maatta and Jarkko Immonen both scored in the final minute of the opening period to give Finland a 4-2 advantage.
Drew Doughty scored 1:47 into the third period to give Canada some breathing room against the Norwegians. Canada held only a 2-1 lead going into the third period. Canadian goaltender Carey Price had to make just 20 saves in earning the victory.
Canada will meet Austria and Finland will take on Norway in Group B games on Friday. Action in Group C will resume with the Czech Republic facing Latvia and Sweden taking on Switzerland in a meeting of teams with 1-0 records.
The United States and the rest of Group A will have Friday off.