Matt Sing was stopped just short of the line by Mark Calderwood, who was sin-binned for holding his man down, while Sean O'Loughlin did well to stop Thomas Lee over the line.
Just before the hour mark Italy lost prop Martin Castrogiovanni to the sin-bin after he infringed with England five yards out and Wilkinson edged them into a 14-6 lead with a simple kick.
Armitage converted the extras, but found himself in the sin-bin five minutes later for a trip on Mark Cueto and conceded his side's first points of the afternoon when McAlister slotted over a penalty.