"We really met the challenge tonight," coach Rick Tocchet said. "We killed five, six penalties in a row. Guys really willed [the win] and obviously Nittymaki played unbelievable for us."
Malone tapped in an awkward shot that bounced over Jonas Gustavsson moments after John Mitchell nearly won it for the Maple Leafs on a pretty rush, with the puck nearly taking another funny hop into the goal.
Malone's goal stood up after a video review.
Niittymaki turned aside chance after chance while Vincent Lecavalier opened the scoring for the Lightning (5-4-4), who won their first road game of the season (1-4-1).
But Ian White scored a power-play goal at 5:04 of the third period for the Maple Leafs (1-7-5), who have lost four straight games in extra time and remained winless at home (0-4-2) in front of a crowd of 19,301.
The Maple Leafs wasted their first six power-play opportunities, including a two-man advantage for 49 seconds early in the second and another in the final minutes.
"We have to persevere, we can't change what we're doing because we're right there knocking on the door," Leafs coach Ron Wilson said. "We've just got to find a way to knock the door completely down."
One Leafs player that Niittymaki repeatedly turned aside was Phil Kessel, playing his first game for Toronto since being acquired in a September trade with Boston for two first-round picks and a second-round selection. He had been sidelined while recovering from offseason shoulder surgery.
The speedy 22-year-old looked strong on the puck and showed no fear going into the corners when he had to. But Kessel took a hard hit from Mattias Ohlund.
"You've got to give him a double thumbs up for taking a hit like that, a massive hit and coming back and still being a dominant player every shift," Wilson said.
In the second period, Gustavsson played a puck that might have been icing behind his goal and fired it into the neutral zone, where Ohlund picked it off.
The Swedish defenseman charged in and fired a slapshot that Gustavsson kicked right to Lecavalier, who fired the rebound into the empty net at 18:34 of the middle period for his second of the season.
It was the 12th time in 13 games the Maple Leafs surrendered the first goal.
The timing could not have been better for the Tampa Bay captain, who is off to a poor start but showed some flashes of his old brilliance with the entire Canadian Olympic team leadership in attendance.
Kessel, a candidate for the U.S. Olympic team, received a loud ovation each time he touched the puck and often looked dangerous once it was on his stick.
"I had a ton of chances let me tell you," Kessel said. "I've got to find some way to get some of those to go in. First game, got to get better.
Gustavsson and Niittymaki traded saves throughout the game, keeping what could have been a high-scoring affair very tight. Gustavsson set aside 30 shots and Niittymaki 40.
With his fighting major, Niklas Hagman now has nine penalty minutes this season. He had four all last year. ... Kessel, who signed a $27 million, five-year deal, after he was acquired, took Jiri Tlusty's spot in the lineup. Tlusty was returned to the AHL Marlies on Monday. ... Forwards Jamal Mayers and Jay Rosehill and defenseman Jeff Finger were healthy scratches for the Maple Leafs, while defensemen Kurtis Foster, Matt Smaby and Paul Ranger were the Lightning's scratches.