DALLAS -- Radek Faksa made a promise to his 2-year-old son when they were playing together before the Dallas Stars took the ice for Game 7.

Faksa did indeed score in his return to the lineup after missing four games because of an undisclosed injury. His go-ahead goal came on a backhander 44 seconds into the third period, after his son had been taken home, and Dallas beat the defending Stanley Cup champion Vegas Golden Knights 2-1 on Sunday night to wrap up the first-round series.

"I'm happy I did," Faksa said. "And so I can show him the video in the morning, and we can watch it together."

Only captain Jamie Benn and Tyler Seguin have played longer for the Stars than Faksa, a fourth-liner in his ninth season who got his goal from the circle to the left of goalie Adin Hill. Dallas also got another Game 7 goal from 20-year-old Wyatt Johnston.

Jake Oettinger had 21 saves in his second Game 7 victory. He also had the Stars' only penalty, though they killed that off after he was called for tripping Ivan Barbashev in front of the net midway through the third.

"The last period was a clinic. Just so proud of the guys of how we responded," Oettinger said. "It's a long playoffs, and you're going to need different guys to step up at different times. A lot of hockey left, so hopefully a lot more heroes. It's going to be a fun ride."

The Stars, the No. 1 seed in the West, move on to play well-rested Colorado in the second round. Game 1 is in Dallas on Tuesday night, a week after the Avalanche wrapped up their series against Winnipeg with a Game 5 victory.

Brett Howden scored for Vegas, which couldn't pull off another series winner in Dallas, where last year the Knights wrapped up the Western Conference finals with a win in Game 6. Hill had 22 saves in his third game of this series after Logan Thompson started the first four.

The visiting team won the first four games in this series until the home teams held serve the last three.

"There's probably a lot of doubters out there. After Game 2, they probably thought we couldn't come back," Benn said. "A lot of believers in this room, in this organization. And we showed them."

Dallas has won Game 7s in each of its first two postseasons for coach Pete DeBoer, who is now 8-0 in his career in such games with four different teams. That includes the Knights' only Game 7 wins in 2020 and 2021 when he was their coach.

Johnston scored his series-high fourth goal on a wrister from the top of the slot with 5:26 left in the first period after picking off a clearing pass by Shea Theodore that his teammate, Tomas Hertl, missed when taking a twisting swipe at it.

A day after his 20th birthday last May, Johnston became the youngest player in NHL history with a game-clinching goal in a Game 7. He gathered a puck that ricocheted off the back boards in the third period of the Stars' 2-1 win over Seattle in that second-round series.

The goal Sunday against came in quick succession after Vegas had two scoring chances. Oettinger made a tough save to deny Jack Eichel and Jonathan Marchessault then shot the rebound off the left post, and got a hit on Johnston before the Dallas youngster skated to the other end and scored about 10 seconds later.

"I think a couple of our players will probably not sleep tonight, because if you look at what transpired in the game," Vegas coach Bruce Cassidy said. "We hit a post, take them down, they score 10 seconds later. We miss an open net at the end of the second, and they score on the first shift of the third. ... It's a little bit of hockey sometimes when two close teams play."

The series ended with both teams scoring 16 goals.

Vegas, which returned 22 of its 27 players from the Stanley Cup-winning roster, tied it in the second period when Michael Amadio made a crossing pass to Howden, who poked the puck into the open left side of the net behind Oettinger.

The only coach other than DeBoer to win eight Game 7s is Darryl Sutter, who was 8-3 in such games over 182 playoff games in 15 postseasons with four teams.

The Knights are 2-2 in Game 7s. DeBoer was also the opposing coach in their other loss, to San Jose in 2019.

It was only the second time of 16 that the Stars won a best-of-seven series after losing the first two games. The other was the very first playoff series in franchise history, when the Minnesota North Stars were down 0-2 before beating the Los Angeles Kings in seven games to open the 1968 playoffs.