Leading by eight to start the fourth quarter, the Blazers saw their lead dwindle to three points, 94-91, with 1:06 left when Eric Gordon canned a pair of foul shots.
But Andre Miller, Nicolas Batum and Matthews responded with two free throws apiece down the stretch to ice the win.
Brandon Roy added 14 points, going 7-of-8 from the charity stripe, and Miller was 9-for-9 on foul shots en route to 13 points as Portland snapped a six-game losing streak.
The Clippers were led by Gordon's 24 points and Blake Griffin added 21 points and grabbed 15 rebounds in the loss.
2014: The Year in Music [PHOTOS]