DALLAS - Mike Modano skated toward an open net and had to be laughing. This was too easy, too perfect.

After five frustrating years, the Dallas Stars were about to win a playoff series and here he was, the franchise icon, getting to put the final touch on it.

Modano’s simple score came with 3.3 seconds left Sunday night, the capper in a four-goal third period that gave the Stars a 4-1 victory over the Anaheim Ducks, eliminating the Stanley Cup champions and sending Dallas into the second round for the first time since 2003.

“It would be easy to feel good and stop right here, but that’s not the case,” said Dallas goaltender Marty Turco, who took the brunt of criticism for first-round exits in 2004, ’06 and ’07. “For all we’ve been through, we talk about doing what we’re capable of and not just one series. We want to win it all. That’s why it’s been so disappointing over the years.”

Stephane Robidas, playing with a cage covering his broken nose, got the winning rally going with a power-play goal that tied it in the opening minutes of the third period. Just 52 seconds later, he set up Stu Barnes for the go-ahead goal.

Loui Erickson scored with 2:18 left to give Turco some breathing room, then Modano’s goal prompted green and gold streamers to erupt from cannons throughout the arena. Triggermen usually fire at the end of victories, but there was no reason to wait.

“It’s very gratifying for a team that’s been through a lot,” coach Dave Tippett said. “It’s the first step in a mission that we all hope will extend for a very long time. But what it does is it builds a belief system in our group that we can do this.”

Dallas’ next opponent hinges on Game 7 of the Calgary-San Jose series.

If Calgary wins, Dallas will be at home against Colorado. If San Jose wins, Dallas will open on the road against San Jose.

Dallas hadn’t won a series since a first-rounder over Edmonton in 2003 and hadn’t closed a winning round at home since the conference finals all the way back in 2000, when the club played at a different arena.

One of the stalwarts on the ’00 team, and the 1999 club that won the Cup, is Brett Hull, now the team’s co-general manager. The other main man then — and now — is Modano, who despite his boyish looks is actually the team’s oldest player.

While he laughs off the idea of being an elder statesman, Modano is happy for the veterans who’ve been through the rough times and for the kids in the locker room, primarily the three rookie defensemen who more than held their own this series.

“This feels pretty good right now,” he said. “Our young guys did great and it’s nice to see them experience success like this.”

The Ducks are the fifth straight defending Stanley Cup champions to fail to make the second round. The NHL hasn’t had a repeat winner since Detroit in 1997-98. No defending champion has even made the finals since the Stars in 2000.

“It’s disappointing because we believe we could do better,” said Anaheim defenseman Scott Niedermayer, the Conn Smythe winner as MVP of last year’s postseason who retired then decided to return to chase another Cup. “Our sights were set higher than this.”

Anaheim trailed this series 2-0 and 3-1, but made things interesting. The Ducks led 1-0 early in the second period on a goal from Corey Perry and it seemed like a good omen for a Game 7 in Anaheim; the team that scored first had won every game so far.

But the Stars dominated the third period. The Ducks had only one shot the first 15 minutes, then Turco handled tough chance after tough chance down the stretch.

“There were a couple of games where we just couldn’t mount much of an attack,” Ducks captain Chris Pronger said. “You’ve got to give them a lot of credit, but part of that falls on us, too.”

Coach Randy Carlyle blamed it on a lack of execution.

“It’s hard to understand,” he said. “It’s so fresh in your mind that we’re not playing past April 20 when we played into June last year. ... You try to create those elite organizations that compete consistently into May. For various reasons, we weren’t able to get that done.”

Dallas grabbed control of the series by scoring on eight of its first 18 power-play chances. Then the Stars went 0-for-18. The drought ended when Modano ripped a shot wide of the net and Robidas knocked the carom past Jean-Sebastien Giguere for his first career playoff goal. On the very next shift, he skated right at Giguere, then fed Barnes for a shot right in front of the crease. The 37-year-old Barnes was so happy about his goal that he gave a flying chest bump to the glass.

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“Robi got by a couple guys and found me in the slot and all I had to do was put it in,” said Barnes, who also had the winning goal in Game 4.

Perry scored a relatively soft goal early in the second period to put the Ducks up 1-0.

Perry was Anaheim’s leading goal scorer this season, but then he sliced a thigh and missed six weeks, returning for Game 4. At game’s end, he was doubled over at the blue line for several seconds, hardly moving, realizing all the months of healing time now ahead of him.

Notes: The road team won the first three games of the series, then the home team won the next three. ... Both goalies had an assist in this game. Turco’s came on Modano’s. ... Ducks D Rob Niedermayer made the trip, but was scratched. He’d been out since a concussion in Game 2. ... This was the third time in franchise history the Stars have eliminated a Cup champion, the first since moving to Dallas. The Minnesota North Stars did it to Montreal in 1980 and Edmonton in 1991.