The Wall-Webster play with 42 seconds remaining put the Wizards ahead to stay and enabled them to snap a four-game losing streak.
Wall also scored 14 points while Bradley Beal added 25 and Nene sealed the win with a pair of free throws, finishing with 20 points.
Webster, subbing for the injured Trevor Ariza, canned five 3-pointers en route to 17 points.
Kevin Love supplied 25 points, 11 rebounds and four assists for the Timberwolves.
Celebrity Breakups and divorces of 2014 [PHOTOS]