"It was not a game that a coach would really like - 7-5 means there was no defence," Sweden coach Bengt-Ake Gustafsson said. "But we are happy to win the second match here, and we have a good chance to win the tournament tomorrow (Sunday)."
Earlier, Russia beat Finland 3-0 with Petr Schastlivyi converting a short-handed breakaway in the second period.
Daniel Fernholm gave Sweden an early lead, scoring from close range at 4:11. Tony Martenson and then Sanny Lindstrom added power-play goals to make it 3-0 to Sweden at 15:26.
Jan Marek scored the Czech Republic's first goal after breaking through two defenders to beat Daniel Henriksson one-on-one.
The Czechs then failed to capitalize on two minutes of two-men advantage.
In the second period, defender Enstrom had two power-play goals for Sweden, while Miroslav Horava, Vlastimil Kroupa and Marek narrowed Sweden's lead to 5-4.
Fabricius, left unmarked near the left post, made it 6-4 off a rebound at 50:54 but Josef Straka revitalized the Czechs' hopes, scoring on a slap shot from the blue line at 55:08 for 6-5.
The Czechs pressed for an equalizer and substituted goalie Adam Svoboda for a field player with 55 seconds left. Fabricius connected to Fredrik Envall's pass near the blue-line and sent it flying across the box into an empty net with 30 seconds left in regulation for 7-5.
Russia dominated play and outshot Finland 36-18.
Center Schastlivyi opened the scoring 18 seconds into Finland's power play at 34:54 when he intercepted the puck in the centre, passed defender Pasi Puistola and beat goalie Petri Venanen with a shot into the top left corner.
It was Schastlivyi's fourth goal in the Euro Hockey tour this season.
Defender Ilya Nikulin made it 2-0 with a wrist shot at 47:06 and former Pittsburgh Penguins winger Alexei Morozov added another goal on a power play with one minute left.
Sweden leads the event standings with 5 points. Russia is second with 4, followed by Finland with 3. The Czech Republic has no points.
Defending Euro Hockey Tour champion Russia is unbeaten in two previous events - the Ceska Pojistovna Cup in the Czech Republic in September and the Karjala Cup in Finland in November. But Russia failed to score in its opener against world and Olympic champion Sweden on Thursday and lost in a penalty shootout 1-0.
Russia tops the Tour standings with 20 points. The win moved Sweden to the second place with 12 points, two points ahead of Finland. The Czech Republic remained at the bottom with six.
The tournament is the third in the European Hockey Tour and is being played at the Khodynskoye Pole arena which hosts 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.