Marc-Andre Fleury made 29 saves, Letang got the only goal in the shootout and the Penguins beat Carolina 2-1 on a night the Hurricanes celebrated their only Stanley Cup championship.
The win was Pittsburgh's eighth in 10 games and gave the Penguins a 2-1-1 lead in the season series.
"I thought there was momentum on both sides tonight," Pittsburgh coach Mike Sullivan said. "They had it for stretches, we had it for stretches. It felt like a track meet on the bench. There was a lot of pace in that game. It's two teams that can skate, and they had a lot of energy tonight."
The game was part of the Hurricanes' three-day celebration for the 10th anniversary of their 2006 Stanley Cup championship. Captain Eric Staal and goalie Cam Ward are the only members of that team still active with the club.
Andrej Nestrasil scored for Carolina with 5:28 left in the third period to help force overtime, and Hurricanes coach Bill Peters said he was happy to get the point.
"When it gets late, gets to those dying moments, it always gets nerve-racking," Peters said. "I thought the guys did a good job staying with it."
Ward made 25 saves for Carolina, which is 1-1-2 in its last four games.
"I think we dominated most of it," Fleury said. "Ward made some big saves. I was trying to keep the puck out of the net and I felt all right."
Phil Kessel put the Penguins ahead at 15:43 of the second by squeezing a shot between Ward and the post from the bottom of the left circle. Former Hurricane Matt Cullen -- also a member of that Hurricanes Stanley Cup team -- assisted on the goal.
"We'd like to play better," Cullen said. "I don't think we had great jump, but sometimes you have nights like that on the road. We just need to find ways to get two points. It's a huge win and a gutsy win and we'll take it. ... It was kind of a special day and it was great to be here."
Nestrasil weaved into the right circle during a rush and tied the game with a shot from there. Joakim Nordstrom had the assist on the goal with 5:18 left.
In overtime, the Penguins put four shots on goal and the Hurricanes had two, but the goaltenders were perfect.
After both teams went scoreless to begin the shootout, Letang beat a sprawled Ward high with a backhand shot in the third round.
Carolina will host the New York Islanders on Saturday night in the second of a three-game homestand, and then on Sunday will play an alumni reunion game featuring many of the Cup champions. ... The Penguins visit Florida on Monday night before returning home on Thursday night against Detroit. ... Carolina D Justin Faulk (lower body) was out, while C Brad Malone and C Riley Nash were healthy scratches. ... Pittsburgh C Evgeni Malkin (lower body) missed his fifth straight game, while LW Sergei Plotnikov and D Ian Cole were healthy scratches. ... The teams' final meeting will be on St. Patrick's Day in Pittsburgh.