Lundqvist made 32 saves, coming within seconds of his fifth shutout this season, to lead the New York Rangers past the Lightning 2-1 on Wednesday night.
"Lundqvist is probably the best goalie in the world right now," Tortorella said.
"It means a lot because we didn't start off too well on the road," Orr said. "So to get confidence on the road and know that we're going to play well, it means a lot."
Rangers defenseman Michal Rozsival, who has seven goals in 21 games this season, sat out with an undisclosed injury. The team said Rozsival could return for Friday's game at Florida.
Tampa Bay center Vincent Lecavalier had his team-record streak of eight multipoint games snapped. He had seven goals and 21 points over the stretch.
Michel Ouellet scored with 16.7 seconds left in the third for the Lightning, who have dropped two in a row after a five-game winning streak. The goal prevented Lundqvist from earning his 12th career shutout.
"It's always tough to lose a shutout like that, when it's close and it felt like I had a good shutout going here," Lundqvist said.
Rangers coach Tom Renney took the blame for the lost shutout bid.
"If anybody should be disappointed, it should be me," Renney said. "I need to protect Henrik with maybe a little different personnel out there late in the game. I owe him a better coaching effort than that, quite honestly."
Tyutin put New York ahead 1-0 from just inside the blue line at 8:51 of the first, the sixth straight Rangers goal scored by a defenseman. Blair Betts had an assist for his first point in 28 games.
Holmqvist had 27 saves.
"I have no beef with the hockey club," Tortorella said. "We just couldn't score a goal."
The Lightning nearly tied it at 1-all five minutes into the second, but Jan Hlavac's shot hit the post.
Orr, a fourth-line enforcer, snapped his 25-game goal-scoring drought to make it 2-0 at 2:04 of the third.
"The entire bench went nuts when Colton scored," Renney said. "First of all, he used (teammate Brendan) Shanahan's stick, and everybody was pretty happy about that."
Lundqvist made a strong save with 15 minutes left on Martin St. Louis' shot from the slot during a power play. St. Louis also had his eight-game point streak (6 goals, 15 points) ended by New York.
Tampa Bay lost a potential goal with 3:28 to play after a video review. It was ruled that Shanahan used his glove to prevent Vinny Prospal's shot from crossing the goal line after the puck trickled past Lundqvist.
"I really think that it was about halfway over the line," Shanahan said. "I swiped it back under Hank. It was on its way, but it didn't cross over the entire goal line."
- Tortorella was fined $10,000 by the NHL for negative comments he made about the on-ice officials after Monday's 4-3 overtime loss at Atlanta. He declined comment after Wednesday's game.
- Rozsival had three goals in his previous two games.
- Tampa Bay recalled D Dan Jancevski and LW Mathieu Darche from Norfolk of the AHL. Jancevski replaced D Paul Ranger (shoulder), while Darche took the spot of RW Jason Ward (healthy scratch) in the lineup.
- Orr's goal was also his first point in 26 games.
- New York rookie D Ivan Baranka assisted on Orr's goal for his first NHL point.