The Wizards closed within a point when Kevin Seraphin scored on a layup with 3:02 to play, but the Clippers ran off eight straight points that began with Collison's drive to the basket with 2:43 left.
Los Angeles won its fourth in a row with Blake Griffin's 29 points and nine rebounds leading the way. The Clippers had to fight off the Wizards after owning an 11-point lead at halftime.
Washington finished a four-game road trip with a 2-2 record and will now return home for five games -- the first of them against the streaking Oklahoma City Thunder on Saturday.
Bradley Beal scored 20 points to pace the Wizards.