"It's incredible. I don't think I realize it yet," Chiasson said. "You work so hard when you're young, and you don't realize that one day this could happen. I was a Montreal Canadiens fan growing up and watching Saku Koivu -- and now I'm playing against him.
"These last couple of days have been really memorable for me."
Chiasson had 13 goals this season for the Stars' AHL affiliate.
"The reason you play in the American Hockey League is to make it up to the NHL," Chiasson said. "Luckily, I've made it up here, and now I've got to work to stay here."
Kari Lehtonen made 27 saves to help end Dallas' three-game skid. The Stars, whose four-year playoff drought is the longest in franchise history, are five points behind eighth-place St. Louis in the Western Conference. But Dallas would have to overtake four other teams that are separated by one point.
The Pacific Division-leading Ducks beat the Stars 4-0 on Monday at Dallas and 5-2 on Wednesday at home. But they had to play this one without captain and leading scorer Ryan Getzlaf, who sustained a lower-body injury during the third period Wednesday.
Matthew Lombardi played his first game with Anaheim following Wednesday's trade with Phoenix.
"We missed some Grade A chances," Ducks coach Bruce Boudreau said. "I mean, Saku missed two or three in the first period, Teemu [Selanne] missed an open net on the power play, and Matthew Lombardi had a breakaway and didn't score. So there were a lot of plays we missed that were uncharacteristic misses.
"When you don't take advantage of your chances, it usually ends up biting you in the butt."
Nystrom and Chiasson scored less than 5 1/2 minutes apart to give Dallas a 3-1 lead with 48 seconds left in the first period.
Fiddler lifted the puck out of the Dallas zone, while the Stars were short-handed, and Fasth came far out of his net in an attempt to poke it away from the oncoming Nystrom. But the six-year veteran got position on Corey Perry, and flipped it over the goalie's outstretched stick and into a wide-open net at 13:54 of the first.
"I think he guessed wrong. It was just bad timing," Boudreau said. "But he made an awful lot of saves to keep us in the game. That's the first time he's done that this year, so we'll give him a mulligan on that one."
The 30-year-old goalie took the blame for his gaffe.
"I misread the speed of the puck or maybe I overestimated my skating ability," Fasth said. "But we all know it was a bad decision by me.
"Those things happen, and unfortunately it happened tonight in a tight game and ended up being the game-winning goal."
MacDermid opened the scoring at 9:03 with a short backhander after Antoine Roussel found him cruising down the slot. The lead lasted just 18 seconds, as Cogliano converted a centering pass from behind the net by David Steckel after the puck took a strange bounce off the end boards on a dump-in by Bryan Allen.
"We didn't help ourselves, but that was [Dallas'] best effort," Boudreau said. "We knew if they scored the first goal and had a lead coming out of the first period, they were going to be very tough. It seemed like after we tied it up, for about 10 minutes we fell apart and started watching them pass the puck.
"Once they got the 3-1 lead, they played pretty solid the second and third periods."
MacDermid sustained an upper-body injury on his first shift of the second period and didn't return.
The Stars and Ducks played their final game as division rivals, due to the realignment of the NHL in 2013-14.
MacDermid's first NHL goal on Wednesday came on the 31st anniversary of his father Paul's first NHL goal. They are the second father-son duo to score their first goals on the same date. The other was John "Peanuts" O'Flaherty and son Gerry, who accomplished the feat on Nov. 3 in 1940 and 1972. … With Jonas Hiller sitting out the game because of illness, the Ducks shifted their backup goalie. Jeff Deslauriers was at the end of the bench for the first 3:57, and Igor Bobkov replaced him. … The Ducks are Lombardi's fifth team in five seasons. He had about 12 1/2 minutes of ice time, had only one shot and was a minus-1. … The Ducks, who came in with the league's third-best power play, were 0-for-4. … The Ducks outshot the Stars 28-25. Dallas hasn't outshot an opponent in nine games.