The Timberwolves managed only two points during the final 4 minutes after taking an 86-84 lead on a layup by Alexey Shved.
Butler's long-range shot put the Clippers in front 90-88 and they went on to capture their second straight. Butler scored 19 points, Jamal Crawford had 17 and DeAndre Jordan contributed 16 points and 12 rebounds. The back-to-back victories have come after the Clippers had lost four in a row.
Los Angeles played its fifth straight game without Chris Paul, who is suffering from a bruised kneecap.
Nikola Pekovic, who had been out of action for six games, scored 17 points with 12 rebounds to pace Minnesota. The Timberwolves have lost six straight and 10 of 11.