Tommy Purdeller nearly tied it on another power play at 3:55 of the third period. A shot from Mikael Frycklund hit the right post and bounced off Skorvanek's back before falling to Purdeller for a shot in the crease, but the goalie got over for a pad save.
"Today it was tough," Skorvanek said. "It was only, like, a one-goal difference almost all the time. So it was tough. ... We're happy with the three points (for the regulation victory)."
Ruzicka, who played 117 NHL games from 2020-24 with the Calgary Flames and Arizona Coyotes, extended the lead to 3-1 at 11:54 with a shot from the slot off a backhand pass from Pavol Regenda.
Gazley pulled Italy to within 3-2 at 16:25, with Clara pulled for an extra attacker. A one-timer from Thomas Larkin struck the back of teammate Giovanni Morini and went in off Gazley's skate. The goal was upheld after a review showed there was no distinct kicking motion.
"The defending, it's a big part of our game," Slovakia defenseman Erik Cernak said. "Unfortunately there was one of the penalty kill and one at 6-on-5, you know? Kind of unlucky. ... We give them some chances, some odd-man rushes. I think we just have to be better against Sweden."
Slovakia can clinch first place in Group B with at least one point against Sweden. The top three teams in each group and the best second-place finisher will receive automatic byes into the quarterfinals.