It was a satisfying end to a four-game road trip for the Ducks (2-1-1), who play Dallas twice at Honda Center on Wednesday and Friday.
Anaheim improved to 24-7-5 (53 points), including an 11-3-5 record on the road.
Bobby Ryan (PPG at 10:13), Corey Perry (12:52) and Matt Beleskey (15:02) each lit the lamp in that pivotal second period, and Selanne slid one into the empty net from center ice with 28 seconds remaining to polish off the victory.
Viktor Fasth tossed the shutout with 26 saves in his first game action in a week. It was the first time the Ducks shut out the Stars in 60 games in Dallas in both the regular season and playoffs.
Despite having to travel, it was the Pacific Division-leading Ducks that displayed more energy and passion, one night after Dallas coach Glen Gulutzan challenged his team to come out with more urgency and desperation.
The Ducks increased their Pacific Division lead to 10 points over the Kings, and remain just four points back of the Western Conference-leading Blackhawks.
Kari Lehtonen, making his 15th straight start, came up with 26 saves for Dallas, which is 1-3-0 in its last four outings - allowing 16 goals in the process.