The Blues ended their third five-game losing streak of the season thanks to Halak breaking out of a recent slump. He had given up four goals in three of his previous four starts.
Michal Handzus scored the lone goal for Los Angeles 5:37 into the second period to create a 1-1 tie but Reaves produced his second score of the season with 5:44 to go in the stanza.
Alexander Steen gave the Blues an insurance goal with 1:04 to go in the second.
Jonathan Quick allowed three goals on 21 shots to take the loss. The Kings have dropped two in a row.