Niemi, who made his eighth appearance, has started three times since Nov. 7. He has allowed only one goal, posted two shutouts and stopped 80 shots in those games.
"You don't want to feel too confident, but I feel pretty good," Niemi said. "I've never played so many shutouts. I've had good stretches, but not like this.
"We had it pretty easy today. It was not too hard for me."
The Lightning dropped to 0-3-1 in their past four. Tampa Bay has scored only 13 goals in a 1-6-2 slide.
Niemi was busier in his previous two starts, He stopped 30 shots in a 1-0 victory at Vancouver on Nov. 22, and 32 in a 2-1 overtime victory at Pittsburgh on Dec. 5.
Chicago coach Joel Quenneville likes the way the 26-year-old Niemi complements No. 1 goalie Cristobal Huet.
"It's been a nice one-two punch," Quenneville said. "Niemi's solid. You see his size and his presence in the net. He challenges and his rebound control is in order.
"The last two starts he might have been overworked. Tonight, he did what he had to do. He keeps himself ready whether he's out for two weeks or out for a week."
Kane left the game with 6:59 left in the first period due to a cut above the eye and didn't return. He landed hard after Tampa Bay's Matt Smaby tripped him along the boards.
"It's not bad," Quenneville said, "They had to stitch it up."
Antero Niittymaki stopped 25 shots for the Lightning.
"When you're losing, you've just got to keep believing in the locker room you can win," Tampa Bay coach Rick Tocchet said. "When there's pressure, it just seem like we cave in certain situations."
In addition to ill-timed defensive breakdowns, the Lightning was doomed by an inability to sustain offensive pressure and generate rebounds.
"It's been one-and-done and it's hard to score in this league like that," forward Martin St. Louis said.
Both teams continued to struggle on the power play. Tampa Bay went 0 for 5 and has failed on 13 consecutive chances. Chicago went 0 for 7 and has scored on one of its past 19 advantages.
Kane scored the lone goal of the first period at 7:42 when his high wrist shot from the right point beat Niittymaki and clanked in off the left post.
Hossa had beaten Niittymaki with a close-in move about three minutes earlier, but Smaby swept the puck away as it reached goal line.
Niemi made two close-in saves on Tampa Bay's James Wright 4:15 into the second. About eight minutes into the period, the Lightning's Steven Stamkos hit the post with a shot.
Eager made it 2-0 midway through the second when he was left open at the edge of the crease and converted Hossa's centering pass. The goal was set up when Tampa Bay defensemen Matt Walker and Victor Hedman both committed to Hossa, who dished the puck to Eager from the right corner.
Hossa extended Chicago's lead to 3-0 with 15.3 seconds left in the period. While skating through the left circle, Hossa pulled Patrick Sharp's deflected centering pass from the air, dropped it to the ice, and whacked the puck past Niittymaki.
Toews made it 4-0 at 6:01 of the third when he chipped in a rebound of Dustin Byfuglien's shot from the slot.
Niittymaki made a pad save on Troy Brouwer's penalty shot with 1:40 left in the third. Brouwer was awarded the attempt after being pulled down by Hedman.
- Tampa Bay D Lukas Krajicek and D David Hale were healthy scratches for the second successive game.
- Chicago D Jordan Hendry was a healthy scratch.
- Actor Jim Belushi dropped the ceremonial first puck.
- The crowd of 21,081 was the Blackhawks 67th consecutive sellout.