Pat Maroon and Nicholas Paul each scored, and Brian Elliott made 25 saves for the Lightning (24-11-1), who began a three-game road trip that continues Wednesday at the Minnesota Wild.
"It's great; we've got another big game [Wednesday]," Killorn said. "Obviously, a loss tonight would have been difficult going into a back to back."
Seth Jones scored, and Alex Stalock made 25 saves for the Blackhawks (8-25-4), who have lost five straight and 13 of their past 14 games.
"It's a fine line," Jones said. "We're not going to accept losing by any means, these results that we're getting. But at the same time, we're not going to do ourselves any favors by coming into the rink every day and pouting about it and hoping that someone comes to save us.
"It's got to be within the leaders in this room and really everyone in this room to play a little bit better every night, bring a little bit more, and that's the only way we're going to get through this."
Chicago played the third without forward Patrick Kane because of an undisclosed injury. Blackhawks coach Luke Richardson said Kane was still feeling the effects of a hit from forward Evgeny Svechnikov during a 5-2 loss to the San Jose Sharks on Sunday.
"I talked to him before the game, he seemed fine," Richardson said. "But when you get into the game and start banging around, things flare up. So, I think it got worse probably as the game went on.
"He's getting checked out tonight, so we really don't know much until tomorrow probably when he'll see the doctors here tonight and tomorrow and get an update on that. He got hit last game. Nothing huge or major, but [he] just felt it a bit and then he felt it that it came on more today."
Jones gave Chicago a 1-0 lead with a power-play goal at 4:50 of the first period when he tapped a feed from Taylor Raddysh past Elliott.
Maroon tied it 1-1 at 11:24, redirecting Victor Hedman's shot from the left point.
