The Wizards faded away after drawing within one on a dunk by Emeka Okafor with 1:49 to play. Washington did not manage another point, missing four shots and turning the ball over once the rest of the way.
Minnesota snapped a six-game losing streak, getting 16 points from Derron Williams and 15 from Ricky Rubio.
Barea pushed the Minnesota lead to 85-82 with 25 seconds left on a layup and Ridnour's free throws came with 11 seconds remaining.
Washington, which had won four of its previous six, was led by John Wall with 19 points. The Wizards scored only 14 points in the second period while making 4-of-15 shots.