The Italians won the opening game of the Pool D round-robin portion of the tournament. The United States and Canada will also take part in Pool D with the top two teams advancing to the next round.
Italy faced a 5-4 deficit heading into the ninth, but put runners on first and second with one away against closer Sergio Romo.
Rizzo then hit a fly ball to left that popped out of the glove of Edgar Gonzalez. It was ruled a double and both runners scored.
Nick Pugliese was credited with the win after pitching 1 1/3 innings of hitless ball.
Italy will return to action Friday with a day game against Canada and Mexico will take on the United States during the evening in what will be the Americans first competition in the event.