Sean Avery, Matt Moulson, Brian Willsie, Eric Belanger and Konstantin Pushkarev also scored for Los Angeles. Derek Armstrong added three assists.
Ryan Getzlaf had the Ducks' goal.
Playing their first game with new coach Marc Crawford, the Kings used four power-play goals to spoil the home debut for the new look Ducks, who aside from dropping "Mighty" from their name have new uniforms and a new logo.
After Avery scored on a rebound 8:02 in, Dallman drilled a 50-foot slap shot past Anaheim starting goalie Michael Leighton during a power play 3:45 later to make it 2-0.
Getzlaf beat Kings starter Mathieu Garon with a shot from the right circle 58 seconds into the middle period to draw Anaheim within a goal. But Dallman assisted on a deflected power-play goal by Moulson at 7:55 of the frame, and netted his second of the game 5:05 later to push the lead to 4-1.
The Kings scored four goals against Ilya Bryzgalov, who replaced Leighton midway through the second period.
Dallman was a free agent signed to a two-year deal by new Kings general manager Dean Lombardi on July 10.
The teams will meet in Los Angeles next Monday before opening the season in Anaheim on October 6.
Both teams skated without their top offseason defensive acquisitions, Chris Pronger for the Ducks and Rob Blake for the Kings.