The U.S. struck first late in the opening period when Garrett Roe kept a loose puck in the Slovenian zone, carried it behind the net and fed Brian O'Neill who was streaking into the slot.
"Once we scored the first goal we really started to fly on the ice", Mursak told NBC's Pierre McGuire after the game.
Ryan Zapolski made 22 saves as the United States failed to protect a two-goal lead in the final period.
Up next for the Americans is Slovakia in another preliminary game. Ceresnak's slap shot from the point found twine to capitalize on a power play and give his team a third-period lead against the gold-medal favorites. The Americans outshot Slovenia 11-3 in the first period.
With some pressure on, after a penalty to US captain Brian Gionta, Slovenia pulled their goalie for an extra attacker.
Kroselj made a handful of quality saves to keep Slovenia in the game, and Zapolski had to do the same in the second period, stopping Urbas on a one-timer with Greenway in the box and the USA on the penalty kill.More news: Senate GOP, Dem leaders say it's time for immigration deal
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Zapolski got out of position after lunging to his left on a save.
In overtime, Mursak was left alone in front of the U.S.net to score the game-winning goal off a pass from Gregorc.
Slovenia captain Jan Mursak, a former draft pick of the Detroit Red Wings, scored that tying goal.
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Returning to the lineup later in the season, he had trouble finding any playing time, the Red Wings put him on waivers and Mursak signed with Amur Khabarovsk of the KHL.
It wasn't the only surprise of the night, though the U.S. like all the other teams is playing without National Hockey League players for the first time since 1994. Olympic upsets happen, and the United States was on the wrong end this time.