First, there was a breakaway, but Carolina goalie Justin Peters got square to the puck.
Moments later, he put shots on goal during a power play.
Then, with the Lightning clinging to a 1-0 lead with less than nine minutes remaining in the third period, Stamkos buried a difficult chance off an Alex Killorn pass.
"If you're going to tell me that the one Steven Stamkos is going to score on was that chance," said Lightning coach Jon Cooper, not bothering to finish the sentence.
His point was clear. Stamkos had easier bids among his nine shots.
"I thought they stayed with it," Cooper said. "We had chance after chance. I've got to give their goaltender a lot of credit. I thought he was exceptional tonight."
In the end, though, it was Lightning goaltender Ben Bishop who was flawless, stopping 31 shots in a 3-0 shutout. It was Bishop's second shutout in two career appearances against Carolina. He also blanked the Hurricanes in April in his Tampa Bay debut, stopping 45 shots at PNC Arena.
"I thought the guys did a great job in front of me," said Bishop, who has four career shutouts. "There were a lot of shots from the outside. In the third period, we got the two-goal lead, which was nice, and they got a few more chances."
Peters kept his team in the game, while Carolina struggled to find any kind of offensive rhythm. And while Stamkos appeared to be having the ultimate night of frustration, Tampa Bay's leading scorer wasn't the least bit rattled.
"No, that was fun," Stamkos said. "I've learned over my career, you can't get frustrated. The first couple years, if you don't score and you get down on yourself, it kind of ruins your game a little bit. I was joking on the bench with the guys, laughing. That's fun. It means you're doing something right."
Tampa Bay extended the lead to 3-0 with less than three minutes remaining when Killorn finished a 2-on-1 on a pass from Martin St. Louis, who assisted on both third-period goals. Killorn, who has played occasionally with Stamkos and St. Louis in the past, was bumped up to the top line for the game.
"Last year, I played with them a little bit, so I have a little familiarity," Killorn said. "It's pretty easy to play with those two guys. I just want to get them the puck and go to the net, make strong plays. They open up the ice for guys like me."
The trio combined for 19 shots on goal, earning Cooper's praise.
"I thought that line was outstanding," he said. "They were a big reason we got two points."
The game reached the midway point without any scoring. In fact, it appeared Cooper's pregame message of firing more shots was lost on the Lightning the early part of the game, as they settled for three shots in the first 20 minutes.
"We had a long, heartfelt talk between the first and second (periods) about getting pucks on net," Cooper said. "We definitely found a way in the second and third."
Tampa Bay opened the scoring at 11:38 of the second period. Victor Hedman fired a shot off the end wall, looking for the puck to find its way to the slot. Instead, it hit the back of Peters' pads and caromed into the net.
"There was a guy coming out on me, so I wanted to hit it as hard as I could on the boards," Hedman said. "I got a bounce, and (Peters) was down on his knees. I was lucky enough to have it go in."
With a fourth straight loss, the Hurricanes fell to 4-6-3. During the tailspin, they have scored four goals.
"We just have to man up," Hurricanes coach Kirk Muller said. "I thought our goalie was good tonight, but he didn't win the game. I thought our five-on-five was good, but we lost our five-on-five. I thought our power play was good. They moved it around and did all of the stuff they were supposed to do, but they didn't score a goal. I think what we need to do is stay the course."
Tampa Bay has no such issues. With a 9-4-0 start, the Lightning have the luxury of some early-season breathing room.
"It is a tough league to come back," Cooper said. "You can't fall behind. You've got to win the ones in October and November if you want to give yourself a chance. So far, so good."