The win takes the Tre Kronor top of the standings in their group after Finland beat Austria 2-1 in the curtain-raiser earlier this afternoon.
Sweden - boasting 18 National Hockey League players in their 20-man squad for the match - looked intent on taking top spot from their neighbours, but were made to wait until the 12th minute to break the deadlock.
Slovakia failed to clear their own zone and the puck was pounced upon by Elias Lindholm; he found Emil Heineman down the left side, and his pass across goal was perfect for Mikael Backlund to sweep home.
Last year's quarter-finalists Slovakia were still very much in the tie late in the first period, but any hopes they had of getting to the break within touching distance were dashed in the final 70 seconds.
Marcus Johansson picked up the puck on the blue line and drove towards goal - his shot was saved by Patrik Rybar and rebounded to Marcus Pettersson, who had the wherewithal to find Leo Carlsson in space, and the Anaheim Ducks' man buried number two.
Two became three with only six seconds remaining - Adam Larsson played the puck from behind the net to Jonas Brodin, who unleashed a powerful strike from the right wing, just inside the blue line, which was too hot for Rybar to handle.
Vladimir Orszagh's young side did not capitulate, however, and came out fighting in the second period, yet every one of their nine shots on goal were kept out by Jacob Markstrom.
Once again, Sweden left it until the final two minutes of the period to do the damage - Erik Gustafsson drifted over to the left side and played a shot-pass onto the stick of Lindholm, who deflected in the fourth goal of the game.
Mexican waves rolling around the arena gave proof to the more passive affair in the third period, in which Slovakia did not register a shot on goal until the final few minutes.
There was still time for Sweden to add a fifth - and in some style - in the 18th minute; Pettersson and Rasmus Andersson worked the puck across to Mika Zibanejad, and the New York Ranger played the one-time between his legs while moving away from goal, past the helpless Rybar.
That put the icing on the cake in the 5-0 victory for Sam Hallam's side, who look ready for the challenge of Austria tomorrow.