Alex Goligoski also scored for the Stars, who won their third in a row and pulled to within two points of Detroit in the scramble for the final playoff slot in the Western Conference.
Los Angeles remained in fourth place in the conference, one point ahead of San Jose.
The game remained tied 1-1 after a scoreless second period. But Dallas got to work in the final period.
Whitney broke the tie less than a minute into the period. Fiddler made it 3-1 on a deflection at 7:58 and added his second goal at 13:56. Whitney scored his second goal at 11:06.