Washington goalkeeper Sam Fowler was caught out of position and Reid easily scored his first just moments into the match.
Reid scored again on a header in the 15th minute. A junior, Reid finished the season with nine goals, including a pair of two-goal games.
Washington struggled in the final third after the early Clemson goal put the Huskies on their heels. Clemson goalkeeper George Marks had a pair of saves, including one in the final minutes as Washington scrambled to score.
The Tigers dogpiled in celebration at the final whistle and fans streamed on to the field in a flurry of confetti.