The Kings, who came into the contest averaging a league-worst 2.02 goals per game, outshot the Capitals 35-22.
Clifford was one of five Los Angeles players to score in support of Jonathan Bernier, who turned in 20 saves. Anze Kopitar, Jack Johnson, Jarret Stoll and Justin Williams accounted for the other goals.
Marcus Johansson scored both Washington goals. The Caps have lost two in a row.
Tomas Vokoun stopped 23-of-27 shots in two periods. Michal Neuvirth made seven saves in the third period.
Johansson opened the scoring early in the first period, but Clifford and Kopitar scored to make it 2-1 after one period. Johansson connected at 13:42 of the third period to make it 5-2.