The game-tying goal came with under two minutes remaining.
Team USA burst out of the gates by pouncing on Slovenia in the first period.
USA coach Tony Granato wasn't impressed with his team's energy level at the end of regulation, while OAR captain Pavel Datsyuk preached better attention to defence, especially when holding a lead.
US defenseman Noah Welch aided Zapolski in the first period with a sliding save of his own.
In the second period Jordan Greenway, the first African American to play for the USA men's Olympic hockey team, tapped in a puck that popped loose from a scrum in front of Kroselj.
The U.S. jumped out to a 2-0 lead off goals from Brian O'Neill and Jordan Greenway.
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Rochester's Brian Gionta did not figure in either American goal. After being blanked in its first two games of the preliminary round, Griffin's accomplishment will prove to be a building block for the Korean hockey program.
It is the first Winter Olympic men's hockey tournament in 24 years without NHL players. All 12 teams advance to the single-elimination portion of the tournament, but group play determines seeding; the victor of each group, plus the highest ranking runner-up, earn a first-round bye.
Since 2013 he has been playing mostly in Russia's KHL with CSKA Moscow.
Mursak, who now plays for Frolunda HC in the Swedish Hockey League, was selected by the Red Wings in the sixth round of the 2006 NHL Draft.
"Once we scored the first goal we really started to fly on the ice", Mursak told NBC's Pierre McGuire after the game. Download the Team USA app today. United States of America leads Slovenia 1-0 17:44 in. Bobby Sanguinetti's sharp-angled shot created the rebound opportunity for Greenway. A Noah Welch turnover left Ryan Zapolski out to dry and the U.S.net wide open, but Welch makes up for it by lunging in front of the yawning crease to make the save on a sure goal. Here are the full starting lineups.