Modano scored his lone goal with just under nine minutes to go in the second period to give Dallas a 4-1 lead. He collected a pass in the slot from Brendan Morrow and rifled a wrist shot under the glove of goaltender Steve Shields.
Belfour earned just his second win in eight starts. He kept Anaheim scoreless through the first half of the contest, but lost his shutout bid when Mike Leclerc scored on the power play.
In 36 career games against the Ducks, Modano has 17 goals and 40 assists, while Belfour has posted a 22-7-2 record against Anaheim.
Shields finished with 21 saves but extended his personal losing streak to six games.
2014: The Year in Music [PHOTOS]