Treille was expelled during the second period for a hit to the head on Roman Starchenko and could receive further punishment from the IIHF disciplinary committee, who will review the incident on Monday.
During the game at the Hartwall Arena, fans criticising the cost of tickets had their banners confiscated. Security at the arena told fans the banners constituted a fire risk, Finnish state broadcaster YLE said.
Finland, who are hosting the tournament with Sweden, put in another excellent defensive performance against Slovakia but struggled in front of goal.
They managed only 22 shots, failed to convert on five power plays and had to rely on goalkeeper Petri Vehanen's 26 stops to win the game.
In the late game at the Hartwall, goaltender Tobias Stephan saved a penalty with 4:36 left in the game as Switzerland hung on to beat Belarus 3-2.
Over in Stockholm, Italy sprung a surprise to beat Denmark 4-3 in overtime, and Russia bombarded Norway's goal with 46 shots en route to a 4-2 win in Group B.