Arrieta (12-6) allowed two singles, Andrew McCutchen in the fourth and Starling Marte in the seventh, while striking out five and walking three.
Tommy Hunter and Justin Grimm completed the three-hitter with one inning each as the Cubs (58-47) matched their longest winning streak of the season from May 11-16 and moved 11 games over .500 for the first time since the end of the 2008 season.
In his last nine starts, Arrieta is 6-1 with a 1.38 ERA. He improved to 5-1 in his career against the Pirates.
Rizzo doubled and scored in both the third and fifth innings as the first baseman led the Cubs’ 14-hit attack with the fourth four-hit game of his career.