Kopitar (Los Angeles Kings) gave Slovenia a 1-0 lead at 15:50 of the first period when he scored off a rebound. Ziga Jeglic scored at 17:28 to make it 2-0. Kopitar had the second of Slovenia's three goals in the second period and finished his hat trick early in the third period.
Krystian Dziubinski scored with 2:48 left in the third period for Poland, which hasn't qualified for the Winter Olympics since 1992. Slovenia earned its first Olympic hockey berth in 2014.
Belarus 5, Denmark 2: In the other game at Minsk, Sergei Kostitsyn scored twice in the third period and Belarus won its opener. Kostitsyn, who played in the NHL with the Montreal Canadiens and Nashville Predators from 2007-13, made it 3-1 with a power-play goal at 3:46 of the third period and scored into an empty net with 36 seconds remaining.
Nicklas Jensen (New York Rangers) and Jannik Hansen (Vancouver Canucks) scored for Denmark.
Slovenia faces Denmark and Belarus plays Poland on Friday.
Group E
Germany 5, Japan 0: Germany, with a lineup featuring seven NHL players, scored three power-play goals to defeat overmatched Japan in Riga, Latvia.
Tobias Rieder (Arizona Coyotes) and Tom Kuhnhackl (Pittsburgh Penguins) accounted for two of Germany's three second-period goals. Leon Draisaitl (Edmonton Oilers) had two assists for Germany, which finished with 51 shots on goal. Philipp Grubauer (Washington Capitals) made 13 saves for the shutout.
Latvia 8, Austria 1: Kaspers Daugavins scored two goals and Latvia damaged Austria's hopes of a return trip to the Olympics by winning in Riga.
Daugavins, who has played 91 NHL games for the Ottawa Senators and Boston Bruins, opened the scoring 5:46 into the game and made it 4-1 with a power-play goal at 7:36 of the second period.
Kristers Gudlevskis (Tampa Bay Lightning) made 22 saves, allowing only a first-period goal to Thomas Hundertpfund.
Germany plays Austria, which qualified for the 2014 Sochi Olympics, and Latvia faces Japan on Saturday.
Group F
France 2, Italy 1 (OT): Stephane da Costa scored 27 seconds into overtime to lift France to victory in Oslo, Norway.
Da Costa, who played parts of four seasons with the Ottawa Senators, went top shelf to beat goaltender Andreas Bernard for the win. Cristobal Huet, who played with four NHL teams from 2002-10, made 23 saves.
Italy took a 1-0 lead when Diego Kostner scored a power-play goal 3:20 into the second period. France, which hasn't qualified for the Olympics since 2002, tied it at 5:40 on a goal by Florian Chakiachvili.
Kazakhstan 4, Norway 3 (OT): Norway forced overtime by scoring twice in the final 1:17 of the third period with its goalie pulled, but Kazakhstan disappointed the fans in Oslo when Brandon Bochenski scored 31 seconds into overtime for the win.
Norway pulled goaltender Lars Haugen with 2:28 remaining in the third period and made it 3-2 at 18:43 on a goal by Jonas Holos. With its goaltender again on the bench, Norway tied the game with 14 seconds left when Anders Bastiansen scored a power-play goal.
But Bochenski, who played 156 games for six NHL teams from 2005-10, beat Haugen for the win.
Roman Starchenko scored twice for Kazakhstan. Mats Zuccarello (New York Rangers) had a goal and an assist for Norway.
France plays Kazakhstan and Norway faces Italy on Friday.
