The Clippers had only a five-point lead heading into the fourth period, but limited the injury-riddled Timberwolves to 14 points in the quarter while winning their third in a row and moving to within a game of the Los Angeles Lakers for first place in the Pacific Division.
Griffin had 19 points and 13 rebounds, while Caron Butler contributed 17 points for the Clippers.
The teams combined to attempt 52 shots from 3-point range, hitting just 17 of them.
Nikola Pekovic had 17 points for the Timberwolves, who played without scoring and rebounding leader Kevin Love and also have lost standout point guard Rick Rubio for the season.
Love spent Wednesday night in a Denver hospital after taking an elbow to the head in a game against the Nuggets. He was evaluated for a neck strain and a mild concussion and then rejoined the team in Minnesota amid speculation he might not play again this season.