After Niittymaki made a save on David Booth's breakaway, Steven Stamkos picked up the loose puck and his shot after an end-to-end rush was stopped by Florida's Tomas Vokoun. However, Malone scored his fifth goal of the season when he converted the rebound from near the post to put Tampa Bay up 3-2.
"I looked up and I think they had three guys kind of standing still on the red line," Stamkos said. "I got a shot and I saw the puck trickling by. I was hoping it was going to go in, and it just sat there and luckily Bugsy [Malone] did what he did best and go to the net and jam it in."
Malone has four goals in his last two games.
"I was just lucky enough to tap it in," Malone said.
Niittymaki made 31 saves and was credited with an assist on Malone's goal.
"I actually didn't see the whole play," Niittymaki said. "I was blocked for a couple seconds [after the save], but I saw them score."
Vokoun, who stopped 28 shots, said Stamkos took a good shot.
"It was lying beside the net and their guy just put it in," Vokoun said.
Stamkos and Martin St. Louis had the other Lightning goals.
"That's the best 60 minutes we've played," Florida coach Peter DeBoer said. "I like what we did from a system point of view. We did a lot of things right. We've got to find a way to get a win."
St. Louis' power-play goal from the left circle at 7:18 of the third got the Lightning even at 2.
Horton put the Panthers ahead 2-1 on a rebound power-play goal at 6:33 of the second. Florida had scored just once on the power play in 19 opportunities this season before that.
Florida took a 1-0 lead when Dvorak scored on a two-on-one with the Panthers short-handed at 8:10 of the first. Stamkos tied it with his third goal this season, coming on a power play with 1:28 left in the first.
"The first two periods I don't think we played Tampa Bay hockey," Lightning coach Rick Tocchet said. "A little bit too much riverboat gambling and trading chances for chances. I think Niittymaki was as solid as could be."
Tocchet declined to answer when asked if Niittymaki or No. 1 goalie Mike Smith will start Thursday's game at Ottawa.
Niittymaki, who got the start after beating the Carolina Hurricanes 5-2 in his first game of the season Saturday, stopped another shot by Booth during a first-period breakaway. Vokoun turned aside an in-close chance by Vincent Lecavalier, who had three shots in the first and four overall.
Lecavalier has not scored goal in 12 consecutive games, dating to last season. The Lightning captain did have two assists, giving him five for the season.
Malone scored three goals on Saturday. ... St. Louis had an assist and has a season-opening five-game point streak. He has six assists and nine points over the stretch. ... Both teams scored for the first time this season in the first period.