Sidney Crosby assisted on all three goals. He picked up his 700th point with the second assist, making him the fastest active player to reach the milestone (497 games).
Despite Crosby's productive night on the offensive end, the Penguins captain gave Fleury much of the credit for the win.
"He was our best player tonight and a big reason why we won," he said.
Fleury was pulled 13 seconds into the second period Wednesday against the Toronto Maple Leafs, a game the Penguins rallied to win 6-5 in a shootout. He responded with his third shutout of the season, which ties Ben Scrivens of the Los Angeles Kings for the League lead.
"I think we played a heck of a lot better in front of him. … Tonight, I thought Marc was extremely good," Penguins coach Dan Bylsma said. "It was a bounce back for our team, but for Marc as well."
Chris Kunitz gave the Penguins the lone goal of the opening period on a nifty cross-ice give-and-go. Kris Letang started the play with a pass from near the defensive blue line to Kunitz along the left wall.
Kunitz sent a pass across the ice to Crosby near the right wall and skated toward the net. Crosby hit him perfectly with a return feed, and Kunitz buried a shot into the top half of the net at 6:53 of the first period.
He added a second with an empty-netter with 1:43 remaining in the third period. It was Kunitz's 13th goal of the season. Crosby's third assist of the game pushed his League-leading total to 36 points.
Kunitz leads all NHL left wings in goals and is tied for third among Canadian-born players behind only Tampa Bay's Steven Stamkos, who has 14 but is out with an injury, and Anaheim Ducks right wing Corey Perry, who scored his 14th on Friday.
Kunitz is one of the more fascinating cases among players trying to secure a spot on Canada's roster for the 2014 Sochi Olympics. Based purely on production, he deserves to be there, and his chemistry with Crosby could be considered a big plus. It could also be the reason he doesn't make it -- Canada's management team could conclude he relies too heavily on Crosby to be successful.
Brandon Sutter doubled the Penguins' advantage with a goal from behind the net on the power play at 8:27 of the third period. Sutter was trying to center the puck for Crosby, but his pass from behind the net hit Tampa Bay defenseman Victor Hedman's skate and slipped into the net past goaltender Ben Bishop's right leg.
The Lightning are now 4-4-1 since Stamkos was lost to a broken leg. They have been wildly inconsistent, routing the Anaheim Ducks and New York Rangers but losing by three goals or more three times. They've also failed to score more than one goal in four of the nine games, and counting the game Stamkos was hurt in, it is five of the past 10.
Lightning coach Jon Cooper was not disappointed by his team's effort against Pittsburgh.
"It [stinks] we didn't score a goal. You kind of need those to win, but you've got to give them a little bit of credit. They dictated a little bit of what went on with us, as I thought we did with them at times," he said. "I didn't really think it was a 3-0 hockey game, to be honest."
Bishop had 26 saves for the Lightning, but Tampa Bay managed only six shots on goal in the third period and the team's best offensive chances came early in this contest.
"We did a pretty good job of tightening things up (in the third period) and of getting the next one too," Crosby said.
The victory pushed the Penguins two points clear of the Lightning and one behind the Eastern Conference-leading Boston Bruins.
Crosby seemed more pleased by his team's play than he did with reaching 700 career points. He did, however, discuss the impact missing extended time due to concussions - he sat out the majority of the 2010-11 and 2011-12 seasons -- has on his feelings about reaching such milestones.
"It's a nice number," Crosby said. "You try to be consistent. I think with missing time, you appreciate those things more. It's not why you play, but it's nice to get those."
Material from team media was used in this report