Cooke chipped a loose puck high in the air off goaltender Mathieu Garon during a Vancouver power play. Garon couldn't control the puck and Cooke stuffed it under him. Cooke's ninth goal of the season came in the final minute of the second and was Vancouver's third of period as the Canucks erased a 2-0 deficit.
Goalie Roberto Luongo preserved the win when he denied Patrick O'Sullivan's chance from in close with 1:48 remaining and the Kings on the power play.
Markus Naslund added insurance with an empty-net goal in the final minute.
Bryan Smolinski started the comeback and Taylor Pyatt gave Vancouver a 2-2 tie with his career-high 22nd goal of the season.
Derek Armstrong and Dustin Brown counted on the power play for the Kings.
Vancouver (48-24-7) improved to 103 points, one shy of the club record. They also maintained their three-point lead over second-place Minnesota Wild and have a game in hand.
Vancouver can clinch first in its division and the third playoff seed in the Western Conference by winning one of its three remaining games.
The Kings (26-40-14), out of the playoffs for the fourth straight season, lost their fifth in a row.
Armstrong gave Los Angeles a 1-0 first-period lead after the Canucks killed a 38-second two-man advantage. He got behind the Vancouver defence to take a break-in pass from Jaroslav Modry and beat Luongo with a low shot.
Luongo gave up a rare soft goal to Brown, who banked the puck in off the Vancouver netminder from a near-impossible angle early in the second.
Smolinski started the Vancouver comeback with a power-play goal two minutes later when Henrik Sedin found him alone in the slot. Pyatt was on Garon's doorstep when he tipped in Jan Bulis's centring pass.
NOTES: The game matched the best (Vancouver) and worst (Los Angeles) penalty kills in the league . . . Defenceman Sami Salo returned to the Vancouver lineup after missing five of the last six games with a groin strain . . . Mattias Ohlund (lacerated elbow) is expected to return to the Canucks' blue-line Thursday against Colorado. He has missed five games . . . Yannick Tremblay was reassigned to the AHL's Manitoba Moose . . . The Kings were also missing key members of their defence corps with Rob Blake (neck strain) and Lubomir Visnovsky (ankle) on the shelf . . . Los Angeles recalled forward Lauri Tukonen from Manchester of the AHL.