O'Donnell's first goal in 158 games came on a one-timer through traffic with 4:33 remaining in regulation.
Ryan Potulny and Sheldon Souray both registered a goal and an assist for Edmonton. Jeff Deslauriers stopped 23-of-26 shots.
After Richardson scored the only goal of the first period, Brown extended the Kings lead to 2-0 at 3:44 of the second by knocking in the rebound off a breakaway shot by Richardson.
Souray cut the lead to 2-1 with a one-timer off a faceoff with 7:43 left in the second period. Potulny tied the game 3-3 at 3:43 of the third period on a power-play goal from the right circle.