Eriksson, named in Sweden's team for the Vancouver Olympics next month, scored once in the first period and twice more in the second to lift his season tally to 16.
"I had a lot more chances out there," Eriksson told reporters. "But it's always fun to score a hat-trick, especially when you win."
Stephane Robidas and fellow Canadian Brad Richards also scored as the Stars (18-11-11) posted back-to-back wins for the first time since late November.
Dallas goaltender Marty Turco made 31 saves against the Ducks (16-17-7), who were playing without leading goalscorer Ryan Getzlaf, sidelined after cutting his leg with his own skate last weekend.
"Somewhere along the way in the first period we lost our composure," said Anaheim forward Bobby Ryan. "These games should be easy to get up for, and for whatever reason we're not coming through."
Jonas Hiller recorded 37 saves for the Ducks, who were out-shot by Dallas 42-34.
Mike Brown also scored for the Ducks.
(Editing by Peter Rutherford)