Neither team managed to score in the first period, but Petr Schastlivyi scored off Igor Volkov's pass at 1:25 into the second period for Russia. It was Schastlivyi's fifth goal in three Euro Hockey Tour events this season.
"We expected them (the Czechs) to play defensively," Russia coach Vyacheslav Bykov said. "They had several scoring chances but our goalie played perfectly and then we managed to open the scoring."
Former Pittsburgh Penguins winger Morozov made it 2-0 on a power play midway through the second.
"We stuck to our defensive tactics in the first period, but we slowed down in the second and could not challenge our opponent," assistant Czech Republic coach Pavel Marek said.
In the third period, Nikolai Kulemin scored from the circle and Morozov added one more from close range to make it 4-0 with 10 minutes to play.
Jaroslav Bednar scored a consolation goal for the Czech Republic on a power play about a minute later.
Sweden was scheduled to play Finland later Sunday.
The tournament is the third in the European Hockey Tour and is being played at the Khodynskoye Pole arena, which will host the world championship next year.
Russia won the tournament in Moscow last year and also captured the Euro Hockey Tour title, edging Olympic champion Sweden in the final.