Rob DiMaio and Stu Barnes had the other goals for the Stars, who climbed within three games to two in the Western Conference semifinal series. Anaheim will have another chance to wrap it up at home on Monday.
Through their first eight playoff games, no one was able to get a two-goal lead on the Ducks as Giguere compiled a remarkable .960 save percentage and 1.27 goals-against average. But he watched the final period from the bench as top-seeded Dallas built a 3-0 lead.
"All I can do is forget about it," said Giguere, who also was pulled in both of his regular-season starts against Dallas. "The next game is a new challenge. This is a learning process. You can't win every game."
"There were a ton of things going on in front of the net that weren't being called. I felt it was imperative to get our guy out," Ducks Coach Mike Babcock said.
DiMaio opened the scoring 9:20 into the first period, producing his first playoff goal in 25 games since the 1999 Eastern Conference quarterfinals.
Stu Barnes made it 2-0 exactly five minutes later and Kapanen added a shorthanded goal with 1:50 to go in the second period.
"We got secondary scoring. We had everyone on board," Dallas Coach Dave Tippett said. "The players that can make a difference did. (Jason) Arnott was excellent, (Pierre) Turgeon was excellent. Those are players who can make a difference in a game, and today they did."
Just three seconds after killing an interference penalty on defenseman Richard Matvichuk, the Stars broke through.
Mike Modano carried down the left side on a three on two and threw the puck in front of the net. Tied up with Adam Oates, DiMaio had the puck hit his right skate and carom past Giguere.
"It's a 20-man team and three or four guys don't have to handle all the scoring," DiMaio said. "This is a deep team, and you're looking to get something from everybody."
Held without a point in the first four games of the series, Barnes doubled Dallas' lead at 14:20 of the first period. Left alone in front of the net, he got a pass from Pierre Turgeon, drifted through the slot and slid the puck under Giguere's left pad.
"It's a different feeling, trailing by multiple goals," Kariya said.
The Ducks had a chance to get on the board when Arnott's holding penalty with 2:51 to go in the second period gave them their third straight power play. But Kapanen scored the Stars' first shorthanded goal of the postseason.
After breaking in ahead of the defense, Kapanen deked his way around Kariya while motoring down the right side. Kariya slowed him down from behind and appeared to direct the puck past Giguere as Kapanen fanned.
"I saw Kariya and thought that maybe I'd have a chance to do something," Kapanen said. "I tried to do what I do best and it was a little lucky, too. But everything counts right now."
Giguere did not last much longer, replaced by Gerber after allowing three goals on 19 shots.
"He's a solid goaltender, obviously," Turgeon said. "He's making big saves. We've just got to put traffic in front of him and shoot the puck. It could be from the corner or from the (side of the) net, but we have to shoot it."
Kariya briefly breathed life into the Ducks when he backhanded the rebound of defenseman Ruslan Salei's shot past Turco from the left side.
But Turco did not have much work thereafter and Kapanen scored again with 4:48 left.
After poking the puck away from defenseman Vitaly Vishnevski, Kapanen broke in alone. He was caught from behind by Salei but managed to flick the puck past Gerber's stick side and into the top left corner of the net.
"Niko was excellent," Tippett said. "He amazes me with how smart he is and how hard he plays. He does it with very little fanfare. He just goes about his business."