One day after being pulled early in the second period of an uninspired loss to Montreal, Fleury stopped 28 shots. Staal had a goal an assist 24 hours after what general manager Ray Shero called a "horrible" game and the Penguins beat the Edmonton Oilers 5-1 on Sunday.
"I've learned it's a long season and there's just going to be some tough ones and bad nights," said Fleury, 3-0 this season in games after being pulled. "You have to be able to put them behind you as fast as possible, forget about it and just move onto the next game."
Shero told the National Post that Staal was "horrible" on Saturday, being a minus-2 with one shot on goal. Staal responded with his fourth multipoint game of the season, going plus-2 in 18 minutes, 54 seconds -- the most ice time among Penguins forwards.
Staal also took a stick to the face while sitting on the bench during Saturday's game.
"It wasn't my best effort against Montreal," Staal said of Saturday's 3-0 loss, "and I wasn't feeling all that great with the way I played. I wanted to come out with a better effort, and I'm glad that things worked out."
Chris Kunitz added two goals, Tyler Kennedy had three assists, and Max Talbot and Zbynek Michalek also scored for Pittsburgh, which reached 40 victories (40-22-8) for the fifth consecutive season and moved to within three points of Eastern Conference-leading Philadelphia.
Ryan Jones scored in the third period for the Oilers (23-38-9), who completed a five-game trip that began with a win in Colorado but ended with four consecutive losses.
"It's been a tough trip. We knew it was going to be a tough trip regardless of our lineup," goalie Devan Dubnyk said.
The Oilers -- 27th in the NHL in goals -- had only two shots in the first period, none in the final 12:40 despite a 5-on-3 advantage that lasted 1:46 late in the period.
"We came out to start this game as spectators," Edmonton coach Tom Renney said. "There was enough of those in the stands. We didn't have to join them. We put ourselves behind the eight-ball right away with how disengaged we were playing."
The kill of the two-man advantage sparked the Penguins, who had scored only eight goals in their previous six home games.
Kunitz's first goal made it 1-0 less than a minute after the 5-on-3 power play expired.
"The momentum was in our favor when the guys killed that off," Kunitz said. "It got the building going and got the guys playing a little better at the end of the period.
"Not too many teams win games if you give up the first goal in this league, so we know it was a great kill for us. It was nice to turn around and score a goal."
Kunitz also had the final goal of the game, giving him 20 this season. He netted his first in three games after missing 13 because of an injury.
Kunitz's goal with 3:49 left was Pittsburgh's first in 23 power-play opportunities over six games, including six on Sunday.
The Penguins -- playing with five defensemen because Matt Niskanen sat out because of flulike symptoms -- beat Edmonton for the fourth time in a row.
Edmonton was much better in the second period, outshooting Pittsburgh 11-10. The Oilers had seven shots in the first 3:30 of the period.
But the Penguins scored twice, beginning with Talbot's eighth of the season 6:27 into the period on a partial breakaway set up by Pascal Dupuis.
Staal made it 3-0 with his eighth with 1:14 left in the second, slamming home a loose puck that was trickling toward an open net off a shot from Kennedy.
"You don't see many bad games from Jordan Staal, and he wanted to come back with a strong one, and he did," Penguins coach Dan Bylsma said. "We needed a rebound game, and he led the way."
So did Fleury, who was denied his 19th NHL shutout when Jones scored 71 seconds into the third period.
"Getting him right back in there to play a strong game, we needed him to rebound," Bylsma said. "And it was a rebound game for our team, and our guys came back real strong."
Cooke's assist was his 300th NHL point. ... Edmonton hasn't won in Pittsburgh in more than five years and the Penguins are 8-2-1 against the Oilers since the 1999-2000 season. ... The Penguins are 36-15-4 when Kunitz is in the lineup, 13-2-1 when he scores a goal, and 23-4-1 when he has a point.