The Timberwolves won their third in a row, finishing the third period on a 13-6 run to take a nine-point lead and then opening a 16-point advantage late in the final minutes.
Pekovic scored 31 points while making 14-of-18 from the field. Kirilenko claimed 11 rebounds to go with his 21 points.
Minnesota hit 53 percent from the field while equaling its longest win streak of the season. The Timberwolves will try to make it four straight on Saturday at home against Dallas.
New Orleans, which has lost six straight, was led by Austin Rivers with 27 points.
Celebrity Families of 2014 [PHOTOS]