The Ducks went after goalie Marty Turco and the Stars and snapped a five-game losing streak.
Koivu scored 4:13 into overtime to give Anaheim a 4-3 victory on Tuesday night. Sexton, a 22-year-old right winger playing in his third NHL game, scored his first two goals -- the second with 62 seconds left in regulation.
"He has proven in college, the ECHL and a little bit in the American Hockey League that he can score," Ducks coach Randy Carlyle said. "He scored two big goals. He probably doesn't realize how big they are for our hockey club.
"He's a young guy who made an impression in training camp -- not big in stature and size, but huge in heart."
Joffrey Lupul also scored, Bobby Ryan had two assists, and Jean-Sebastien Giguere made 19 saves to help the Ducks end a frustrating skid in which they lost once in overtime and twice in shootouts.
"There have been a number of games where we felt that we played well enough to win, when we had leads going into the last 5-10 minutes of the third period and lost," Koivu said. "Now, coming back from behind and getting a big goal in the end by Sexton, those are huge things. Hopefully, this is a turning point."
The Ducks, who rallied from three one-goal deficits Sunday in a shootout loss against Ottawa, spotted Dallas a 3-0 lead before Lupul scored on a breakaway at 18:24 of the second period. Sexton connected with 13:52 left in regulation.
"The first two games I played here, we lost in a shootout. So to win the game in overtime, it's just great," Sexton said. "Our team has been working hard, and to be able to respond from the three-goal deficit -- especially after losing the last two games in heartbreaking shootouts -- it just says a lot about your team."
Lupul was sent in alone by Ryan Getzlaf and he jammed the puck between Turco's pads as the goalie slid into the net with it. It was Lupul's 10th goal this season and fourth in three games, after he missed seven because of back spasms.
Sexton narrowed the gap to 3-2, scoring from the edge of the crease. The Ducks tied it when Sexton beat Turco from a sharp angle.
"I'd say it was probably the coolest feeling. Take my coolest previous feeling and multiple it by 10, if not more. That is what it was," Sexton said. "I thought we were due to score. But once it actually happens, you're in shock. To get another one after that, it just felt like a dream."
Koivu completed the comeback, carrying the puck past Steve Ott at the blue line during a 3-on-1 rush and converting his rebound. It was his 36th winner and first with Anaheim.
Brad Richards scored twice and Mike Modano also had a goal for Dallas. James Neal and Loui Eriksson each had two assists, and Turco made 38 saves. The Ducks outshot the Stars 14-2 in the third period, 7-2 in overtime and 42-22 overall.
"Anytime you have a three-goal lead and you don't bring it home, it's tough," Dallas coach Marc Crawford said. "In the third period, you knew they were going to come and make a push. That is the way they play. You have to want the puck and want to make plays."
In the opener of a five-game road trip, the Stars took a 1-0 lead 9:06 in while Sexton was off for goaltender interference.
Modano made it 2-0 at 11:00 with his 547th career goal. He ended an eight-game drought with a one-timer from the middle of the right circle. It was Dallas' 100th goal against Giguere, enabling the Stars to become the first team to reach triple digits against the 12-year veteran.
Richards scored his second of the game and ninth this season. The frustrated Ducks took three penalties during an 8:38 span before breaking through.
"Any loss is certainly bad, especially when you had a chance to win," Turco said. "I felt like we were doing things a little different in the third period. That is the way it goes sometimes. You've got to trust what you do out there. It is tough one to swallow right now."
NOTES: Sexton set a Ducks rookie record with nine shots. ... The Ducks have had only four power plays in their three losses to Dallas this season. In 30 meetings the previous four seasons, they averaged 5.3 power play opportunities per game. ... Perry's 15-game home point streak ended, two shy of the franchise record set by Paul Kariya during the 1988-89 season. The Stars also snapped Perry's club-record point streak at 19 games on Thursday at Dallas.