The tournament darlings were a surprise group winner and maintained their run at Santagiulia arena as forward Pavol Regenda scored in the first and third periods, while forwards Milos Kelemen, Oliver Okuliar, and Dalibor Dvorsky added goals in the second and captain Tomas Tatar scored in the third.
The 2018 silver medallists, Germany, had cruised past France in the qualification play-off but faltered in attack and will leave the Games empty-handed.
The remaining teams in the tournament will be reseeded at the conclusion of the quarter-finals on Wednesday, with the top seed playing the lowest seed and the second and third seeds facing off in the semi-finals on Friday.
"We were big underdogs, we were hoping to sneak into the quarter-final, and right now we are in the semis," said head coach Vladimir Orszagh.
"The guys are working hard every day, and they know their priorities, why they are here."
The 2022 bronze medallists, Slovakia, struck first as defenceman Erik Cernak rifled the puck from the blue line and Regenda tipped it in late in the first period.
Kelemen cruised around a flailing German defender and flicked the puck into the top right corner of the net four minutes into the second period, and Okuliar beat the goalie to add another score 31 seconds later.
The Slovak fans breathed a sigh of relief as their tournament hero Juraj Slafkovsky returned to the ice after crashing awkwardly into the boards, and Dvorsky added some insurance as he outfoxed the German defence.
German forward Lukas Reichel scored late in the second, and the team put pressure on as they outshot Slovakia 13-12 in the third, but another score from Regenda put it completely out of reach, and Tatar's empty-netter capped off Germany's misery.