Canada improved to 2-0 with the win after shutting out Finland 3-0 in the tournament opener two days earlier.
Matheson opened the scoring against the Italians by converting a cross in the 33rd minute. She then fed Adriana Leon for a tap-in goal 10 minutes later.
Early in the second half, Rhian Wilkinson crossed the ball to Kyle who scored from close range to make it a three-goal game.
"We just started to press them more and once we started pressing them, we were able to win the ball higher up the field," Matheson said.
Cristiana Girelli scored Italy's lone goal in the 51st minute.
The game was chippy at times. Canadian midfielder Sophie Schmidt was bloodied after appearing to take an elbow to the face but was in good spirits afterwards with a bandage on her cheek.
Italy's Elisa Bartoli was handed two yellow cards by the referee. The first came after she tripped up Canada's Christine Sinclair and the second came later in the game after she plowed into Matheson.
Canadian coach John Herdman was pleased with how his team responded to the aggressive style of play.
"The Italians were relentless with their pressure and when you skip a tackle, they'll leave a foot in and bring you down," he said. "And I was pretty pleased with how the girls got a bit testy as well and decided to try and match that pressure and physical intensity."
Canada, which is currently ranked seventh in the world, will wrap up preliminary-round play Monday against No. 11 England at the GSP Stadium in Nicosia. A tie puts Canada into the final and will see England relegated to second in the group as Canada has more goals scored.
Canada has won this tournament three times but has lost in the final the last two years: 1-0 to England last year and 2-0 to France in 2012.