The six straight points from the Clippers turned a one-point deficit into a 90-85 lead with 3:02 to play and Los Angeles held on from there to snap a four-game losing streak.
Chris Paul started the key stretch with a jumper and he made six free throws over the final 30 seconds to secure the victory.
Paul led Los Angeles in scoring with 23 points and added 11 assists. Griffin had 18 points and DeAndre Jordan contributed 15.
The Timberwolves led by as many as nine points during the second quarter, but fell behind by two at halftime.
Kevin Love had 19 points and 12 rebounds for Minnesota, which pulled down 21 offensive rebounds. The Timberwolves outrebounded the Clippers by 17, but Minnesota could not overcome a lackluster 37-percent performance from the field.