Morozov scored twice, including the overtime-winner, as Russia edged the Czech Republic 5-4 at the IIHF World Hockey Championships in action.
Morozov capped an exciting overtime by firing a shot past Czech goaltender Milan Hnilicka. The winning goal came after Kovalchuk failed to convert on a penalty shot earlier in the extra period.
"I don't think the better team won today, I think the luckier team won tonight," Czech Alex Kotalik said.
Sergei Zinoviev, Konstantin Gorovikov and Konstantin Korneyev had the other goals for Russia (2-0).
Patrik Elias scored three power-play goals for the Czechs (1-1), who held a 43-27 edge in shots on goal. Kotalik had the other goal.
The Czechs did a solid job of containing Russia's top line. The Washington Capitals trio of Alexander Ovechkin, Alexander Semin and Sergei Fedorov finished with just one assist after recording three goals in a 7-1 win over Italy on Friday night.
Ovechkin hit the post twice.
"It's luck, my goals aren't coming so they'll come later," Ovechkin said.
Ovechkin said the Russians took too many penalties and gave the Czechs skilled players too many chances to get back into the game.
"There were a couple of big hits but not as physical as it could be," Ovechkin said. "I think right now, teams are trying to get a feel for each other.
"Every game right now is important."
The sellout crowd of 13,109 - which seemingly has adopted the Russian team - helped create a raucous atmosphere, thanks in large part to a very physical and entertaining hockey game.
Zinoviev opened the scoring in the first period, getting a rebound at the side of the net and firing a shot past Hnilicka.
But the Czechs countered with power-play goals from Elias and Kotalik to take a 2-1 advantage later in the period. However, Russia pulled even on a huge power-play goal from Gorovikov when he caught Hnilicka out of position with three-tenths of a second remaining in the first.
Morozov put Russia ahead in the second but it was short-lived. Elias, parked at the side of the net, controlled a wide point shot from Marek Zidlicky and beat Russian goalie Mihail Biryukov to make it 3-3.
Elias and Korneyev traded power-play goals in the third.
"It was a tight-tight game and special teams were a big factor in this game," Kotalik said. "That's probably how it's going to be in the rest of the tournament."
Kotalik said the Czech's are satisfied with the way they played and didn't give up much in five-on-five play.
Kovalchuk was awarded the penalty shot after being hauled down by Czech defenceman Tomas Kaberle. He managed to beat Hnilicka but Kovalchuk's shot went off the post.
Biryukov replaced Alexander Eremenko midway through the second after Eremenko was hurt during a goalmouth scramble. He didn't return to the Russian bench.
Eremenko was having his right knee examined. Russia is already short a goaltender with Capitals prospect Simeon Varlamov injured.
Russian officials are hoping to add goalie Evegeni Nabokov to their roster, should the San Jose Sharks be eliminated from the NHL playoffs.
Phil Kessel had a hat trick and Devils defenseman Paul Martin added an assist as Team USA powered past Slovenia, 5-1, at the IIHF Ice Hockey World Championship on Sunday.
Team USA (2-0) prepares to face Canada (2-0) on Tuesday.