Rizwan and Irfan both suffered hamstring injuries in the third match in Rawalpindi, where a second-string New Zealand side won by seven wickets to level the five-match series 1-1
The 26-year-old left-arm bowler got his first wicket when he trapped Kusal Perera leg-before with the final delivery of his eighth over.
He returned to dismiss Angelo Mathews with the first delivery of his ninth over, getting the rival captain caught at long-off, and bowled Thisara Perera with his next ball to complete the hat-trick.
Faulkner, whose 4-38 in the first one-dayer earned him the man-of-the-match award and helped Australia take a 1-0 lead in the five-match series, finished with figures of 3-45.