Alexei Morozov's hat trick and two assists led Russia past Ukraine 8-1, defenceman Petteri Nummelin scored two power-play goals in Finland's 6-2 win over Denmark, and forward Lee Stempniak scored twice to lift the United States over Belarus 5-1.
As in the 8-2 thumping of Belarus on Friday, the Czechs were ruthless on the power play, converting three times.
Petr Sykora and Hlinka scored in the first period, and the Austrians limited the Czechs to one goal in the second, by Petr Caslava on a power play at 10:02.
Raimund Divis ruined Roman Cechmanek's shutout bid when he wristed the puck from the sideboards over Cechmanek's left shoulder at 17:08.
Michal Barinka, Hlinka, and Jan Marek added third-period goals for the Czechs.
The Czechs, bidding for their third consecutive appearance in the final, will face their first real test of the tournament on Tuesday against the U.S. in final Group B play.
"That will be a tough game, our first real game here," Hlinka said.
The Americans were 3-0 up by the end of the first period against Belarus, with goals by defenceman Jack Johnson and forwards Lee Stempniak and Chad Larose.
Despite the second period becoming a little edgier as Belarus became more frustrated, Chris Clark added a fourth U.S. goal 4:30 in, and while enjoying a two-man advantage, Stempniak banged in his third goal in two games.
Belarus captain Oleg Antonenko delighted the largely partisan crowd when he ended John Grahame's shutout bid, deking defenceman Brian Pothier to flick the puck in over Grahame's shoulder.
"We wanted to give John the shutout so it's a pity," Clark said. "That will be tougher against the Czechs. Two 2-0 teams going at each other."
Ukraine blue-liner Sergii Klymentiev opened the scoring just four minutes into the Group D game against Russia when his slapshot went through the legs of goalie Alexander Eremenko.
But Russia scored two power-play goals in a three-minute span to take a 2-1 lead into the first intermission.
One was Morozov's opener, a rebound into the top corner at 9:38. His second also went top corner on a power play with less than a minute left in the second period. He completed the hat trick at 11:40 in the third, taking a pass from Danis Zaripov and beating the goalie high on the stick side.
Sergey Zinoviev, Ilya Nikulin and Vitali Proshkin also scored for Russia.
"It was a great game for us," Morozov said. "We have a lot of talented players on this team and all our lines are scoring right now."
Russia, bidding for its first world title since 1993, has 17 goals in two preliminary round games.
Ukraine dropped to 0-2 and will face Denmark in its final first-round game on Tuesday. Russia faces Finland, which beat Denmark 6-2 to improve to 2-0.
Nummelin, playing in his 13th world championship, beat Denmark goaltender Michael Madsen with a wrist shot into the top corner on a 5-on-3 at 7:36 in the first period of the Group D game.
Denmark tied the score at 12:49 on another 5-on-3 power play through Jesper Damgaard's low shot from the point.
Mikko Koivu gave the 2006 Olympic silver medallists a 2-1 lead two minutes later with a short-handed goal, and Nummelin's second of the game on another 5-on-3 with just over a minute left in the opening period made it 3-1.
Peltonen scored Finland's third 5-on-3 goal at 3:28 of the second, defenceman Aki Berg scored early in the third, and Jukka Hentunen added another midway through the final period to complete the scoring for Finland.
Denmark got one back on a power play at 5-1 down when Christoffer Kjaergaard took a perfect centring pass from Frans Nielsen and redirected the puck.
Finland will face a much bigger challenge when it plays host Russia on Tuesday.
"Russia will be a big challenge for us," captain Ville Peltonen said. "They have a lot of skilled players and it will take a complete effort. The first two games have been pretty one-sided so this will be a good test for us."
Austria and Belarus will be in a must-win situation on Tuesday. The loser will play the relegation round in an attempt to avoid dropping out of world hockey's elite group. When the pair met at last year's worlds, Belarus won 5-0 and finished sixth.