Bobby Ryan had a goal and an assist, Corey Perry and Matt Beleskey also scored and Ryan Getzlaf added two assists for the Ducks, who completed a four-game road trip (2-1-1). Teemu Selanne capped the scoring with an empty-netter in the last minute.
Both squads were coming off disappointing losses the night before, the Ducks 2-1 in overtime at Columbus and the Stars 3-2 at home against Los Angeles.
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.
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.
After completing a crucial 11-game stretch in which they played nine at home with a 4-6-1 mark, the Stars' playoff chances look to be in jeopardy, as they trail St. Louis by three points for the final Western Conference playoff spot.
Anaheim broke the scoreless tie at 10:13 of the second period on the power play, when Ryan Getzlaf fed a pretty cross-ice pass to Ryan in the left face-off circle, where he unleashed a wrist shot that beat Lehtonen past the blocker for his 10th of the season.
The Ducks needed less than three minutes to push the lead to 2-0 when Perry notched his 12th of the year at 12:52. After Lehtonen made a pad save on Getzlaf's shot from the point, Perry swooped in to pop the loose rebound home.
The hole for the Stars became deeper at 15:02 of the second when Beleskey, who missed the previous four games with an upper-body injury, scored his sixth. After curling out from behind the net for a backhander that Lehtonen stopped, Beleskey dug out the loose rebound from several skates in front and swatted it into the empty side of the net.
The Stars had a prime opportunity to get one back on a power play at 7:30 of the third period, but Fasth made a sliding pad save on Ray Whitney's one-timer from the left side of the crease.
Anaheim almost made it a four-goal lead 26 seconds later when Perry sped in alone, but Lehtonen denied his backhand deke attempt.
Fasth came up with another big save at 11:27 to preserve the shutout when he stopped Alex Goligoski's uncontested wrist shot from the right circle.
The Stars definitely heard some boos during two uneventful third-period power plays from the season's smallest home crowd of 13,748.
In full desperation mode, Dallas pulled Lehtonen for an extra attacker for the final 1:34, but Selanne hit the empty net from his own blue line with 27.1 seconds left.
It took the Ducks just 25 seconds of the opening period to generate their first good scoring chance, when Ryan grabbed a loose puck and fired a wrist shot from a sharp angle that flew over the prone Lehtonen but pinged off the far goalpost.
Less than a minute later, the Stars would hit their own iron, as Loui Eriksson rang a wrist shot from the slot off the left post.
Fasth made a nice pad save on Eriksson at 4:01, denying his uncontested backhander from in front.
The Stars nearly took the lead with 35 seconds left in the first when Jagr set up Jamie Benn in front for a point-blank wrist shot, but Fasth came up with a big pad save.
NOTES: Anaheim made a small trade earlier in the day, sending minor league forward Jay Rosehill to Philadelphia for forward Harry Zolnierczyk, who has played seven games for the Flyers this season but will report directly to AHL Norfolk. ... The Stars assigned LW Toby Petersen to AHL Texas before the game. Petersen had spent the entire season at Texas before coming up to play his first NHL game of the season Sunday against Los Angeles. Dallas also assigned 19-year-old prospect Brett Ritchie to the AHL club after his junior squad, Niagara, was eliminated from the OHL playoffs.