Slovakia's Peter Cehlarik opened the scoring about nine minutes into the game but his goal seemed only to ignite a German side eager to get back on track after Sunday's 5-1 loss to Finland.
Germany's Patrick Hager, Phillip Gogulla and Patrick Reimer all scored during a 10-minute span of the second period before Brooks Macek and Dominik Kahun padded the lead in the third.
"It was a big game today," said German coach Marco Sturm. "We had to respond from the last game. Moving forward, it was a huge win for us tonight."
The win was Germany's first in three games and left them sitting fifth in Group B, one point ahead of the United States and one point behind France. The top four teams after the seven-game group stage advance to the quarter-finals.
Up next for Germany will be a Thursday clash with defending champion Canada, who have outscored their opponents 20-2 through their first three games in Russia.
Slovakia, third in Group B with six points, play again on Wednesday against a winless Belarus team.
In other action, France grabbed their second win with a 6-2 victory over winless Hungary to move into fourth place in Group B while Norway beat Kazakhstan 4-2 to move into a tie for third place with Sweden in Group A.
For Switzerland, it was third time lucky in overtime as they beat Denmark 3-2. After Swiss forward Nino Niederreitter tied the game with two minutes left in regulation, Eric Blum netted the winner with a shot from the top of the face-off circle to put Switzerland one point back of third place in Group A.
(Editing by Frank Pingue)
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