Christensen scored the only goal in the shootout, Fleury had 32 saves and stopped all three shots in the tiebreaker, and the Pittsburgh Penguins beat the Dallas Stars 4-3 Friday night.
The 19-year-old Crosby had two assists in his first game since going scoreless in the all-star game on the Stars' home ice Wednesday.
"I've been here the last five days and the everything has been great," said Crosby, who leads the NHL with 74 points. "It was exciting, a fun game, an intense game. We're happy to win it."
Christensen scored on Pittsburgh's first shootout attempt, and Fleury preserved the win by holding off Dallas' Sergei Zubov, Jussi Jokinen and Mike Ribeiro. The Penguins improved to 2-5 in shootouts and dropped Dallas to 5-2.
"I think the shootout is fun," Fleury said. "We haven't had many wins in it, so this is good for us."
Mark Recchi scored two goals for the Penguins, including the 500th of his career that tied the score at 3 with 8:01 left. He has five goals in his last two games. Crosby had assists on both of Recchi's goals.
But Crosby had some frustrating moments in his regular-season debut in Dallas before Pittsburgh squeaked out its fourth win in five games.
Crosby was originally credited with a goal that gave the Penguins a 2-1 lead at 12:08 of the second. However, the official scorers later ruled that Recchi deflected Crosby's wrister into the net.
With 5 seconds left in the overtime, Dallas' Marty Turco stopped Crosby's solo rush on the right side. He also missed on his try in the shootout. Crosby has failed on all six of his shootout attempts this season.
"I felt pretty good on that one," Crosby said of his shootout try. "I didn't put it where I wanted it. It's a matter of confidence."
Patrick Stefan's goal gave Dallas a 3-2 lead midway through the third. Zubov and Jokinen also had goals for the Stars, who snapped their three-game winning streak.
"We were good at times but not enough to get the win," said All-Star Dallas defenceman Philippe Boucher, who had two assists. "We wanted this one badly but you always have to be on the go against a quick team like theirs."
Zubov, who missed the last three games with an elbow injury, blasted a shot from the left point past Fleury to give Dallas a 1-0 lead with a power-play goal at 11:58 of the first.
Jordan Staal's shot from the left circle beat Turco to tie the score at 8:42 of the second. After Recchi's first goal gave Pittsburgh a 2-1 lead, Jokinen tied the score again with 5:17 left in the period.
Stefan put Dallas ahead at 9:19 of the third before Recchi evened things up again when he chipped in a loose puck over Turco's glove for his 500th goal.
"I was never really supposed to play in this league," Recchi said. "To get that number I'm obviously very proud."
Several players returned from injury for Dallas. Defenceman Steve Ott had missed 37 games with a fractured ankle. Boucher was out two games last week with a facial injury, and centre Jeff Halpern returned after sitting out three contests because of a bad groin.
Notes: Dallas played its 500th home game since moving from Minnesota in 1993. The Stars have a 288-134-65-13 record in Texas. ... Pittsburgh beat Dallas on the road for the first time since 1995. ... Pittsburgh D Mark Eaton played for the first time since Nov. 4 after missing 35 games with a dislocated left wrist. ... Dallas C Mike Modano skated Thursday for the first time since December. Modano has been out since Dec. 4 with a hip injury and is expected to practice Saturday.