Defencemen Drew Doughty and Shea Weber and forward Ryan Getzlaf also scored for defending champions and favourites, whose goaltender Roberto Luongo was rarely tested, stopping 23 shots for the shutout.
Carter started the move that led to his first goal after coming out of a two-minute penalty. The puck then travelled from Sidney Crosby to Patrick Marleau and then back to Carter who fired it home.
Carter's second goal was the result of another turnover as Marleau stole the puck from Austrian goaltender Bernhard Starkbaum behind the net, before picking out Carter who skated out front and scored before Starkbaum could recover.
His third goal followed a goalmouth scramble and handed him a rare ‘natural hat-trick’ (three consecutive goals).
In the other Group B game Finland beat Norway: Teemu Selänne opened the floodgates in a 6-1 win, and in doing so became, at 43 years, seven months and 11 days, the oldest ever scorer in an Olympic ice hockey tournament.
The goal also took Selänne’s overall goals total to 21, which combined with assists gave him a points total of 39, another new Olympic record.
The veteran right wing, known as “The Finnish Flash” due to his speed on the ice, is appearing at his fifth Games in Sochi, and already has a silver and two bronze medals to his name.
Lauri Korpikoski (2) Olli Jokinen, Jori Lehtera and Olli Maata scored Finland’s other goals, with Per-Age Skroder netting a consolation for Norway early in the third period.
Finland and Canada now share the lead in the group and are both guaranteed progress to the knockout phase ahead of their showdown to decide who finishes top.
Earlier in the day, the Group C match between Czech Republic and Latvia saw another veteran right winger, Jaromír Jágr steal the show on the eve of his 42nd birthday. The Czech inspired his team to a 4-2 win, scoring a wonder goal in the first period, and masterminding an offensive display which suggested they could make a real impact in Sochi.
"We didn't play very well in the first half of the game against Sweden, but we played better in the second half of this game, so we have to wait for tomorrow [against Switzerland] to see what kind of team we really are," said Jagr afterwards.
In the day’s other Group C encounter Sweden beat Switzerland 1-0 to preserve their winning start and remain top of the group. The only score of the match coming in the third period, just seven minutes from the end, courtesy of forward Daniel Alfredsson.
Switzerland now lie tied with the Czech Republic on three points, with Latvia yet to win.