Drouin started the play with a drop pass in the right circle for Hedman, who then placed a centering pass on Killorn's stick for the shot that beat Detroit goalie Jimmy Howard on the glove side.
"It was a great play and it's a good thing I have a long reach and a long stick," Hedman said. "[Drouin] is such a skilled guy, and it was great that we were able to get that goal for [Killorn]
Anton Stralman and Steven Stamkos also scored for the Lightning (44-21-7), who are two points behind the Montreal Canadiens for first place in the Atlantic Division and Eastern Conference. The New York Rangers are tied with the Lightning for second in the East at 95 points but have three games in hand.
"We've played well against Detroit and Montreal this season, and that's good," Hedman said. "We've struggled against Boston, and hopefully we can change that Sunday. It's good for the team to play well against these teams and perform in these types of atmospheres."
Goalie Ben Bishop made 30 saves for the Lightning, who are 3-0-0 against the Red Wings this season.
Tomas Tatar scored for Detroit (38-21-11), which trails Tampa Bay by eight points for second place in the Atlantic Division. If the standings remain the way they are, the Red Wings and Lightning would face off in the Eastern Conference First Round of the Stanley Cup Playoffs.
"That's the way it's looking right now, but we'll deal with [the playoffs] when the time comes," Bishop said. "Obviously, these are big games. It's kind of a playoff atmosphere out there and it's always fun when you have a lot of red in the crowd to send them home unhappy."
Howard, who made 29 saves, believes a playoff series between the Red Wings and Lightning would be one of the best in the first round.
"It would be a [heck] of a matchup, that's for sure," Howard said. "It would be extremely tight and come down to the team that gets the bounces."
Detroit has lost four of its past five games.
"I thought we came out strong and really generated some good scoring chances," Red Wings captain Henrik Zetterberg said. "Obviously, this would be the matchup in the playoffs, and we'll have to work harder in these games if that happens. But I thought we battled tonight and had a lot of good moments."
The Lightning took a 1-0 lead at 1:22 of the second period on Stralman's seventh goal. Howard made a pad save on Hedman's slap shot from the point, but Stralman was in front of the net to bury the rebound.
"It was nice to see that one go in," Stralman said. "They are a really good team, and both teams had a lot of chances, but we hung in there and Bishop was really big for us. We got the goals when we needed them, and I'm happy to be part of that."
Tatar scored his 26th goal at 6:57 of the second period on a power play. There was a scrum in front of Bishop as the puck squirted under his pad. Tatar battled Lightning forward J.T. Brown in the crease for the puck and punched it in the net.
"We should be able to score more goals and we had some 'A' chances tonight," Zetterberg said. "We have to take advantage of those chances and score those goals if we want to win these games."
Stamkos scored into an empty net for his 40th goal with 28 seconds remaining in the game.
"We didn't play our best in the first two periods, but in the third I think we turned it up," said Stamkos, who has scored 40 or more goals four times in his seven NHL seasons. "I think it was a combination of us being fresh and them playing last night. We expected it to be a tight game, and that's what it was."