Jacob Trouba scored for the U.S. The Americans need to beat Slovakia on Monday in Group B to move on.
Canada faces Russia on Monday to determine which team gets a bye into the semifinals.
The 19-year-old Nugent-Hopkins was the first pick of the 2011 NHL draft by Edmonton. The center had 52 points in 62 games for the Oilers last season.
Slovakia stayed alive by beating Germany 2-1 on an overtime power-play goal by Peter Ceresnak.
In Group A, Finland beat Switzerland 5-4 on a shootout goal by Markus Granlund, who also scored twice in regulation. The Czech Republic defeated Latvia 4-2 to advance to the next round. Martin Frk scored twice.