Kucherov sat out due to illness as Tampa Bay swept the five-game season series with the Red Wings.
"That's what we talked about before the game, Kuch has been so big for us," Killorn said. "He comes down with something, we need to step up and help him out."
Kucherov was scratched about 90 minutes before the game.
"The guys took it as a challenge," Tampa Bay coach Jon Cooper said.
"I thought we had at least the same amount of chances, but we've got to work for our goals," Red Wings captain Henrik Zetterberg said.
After Sustr put Tampa Bay up 2-1 early in the second, DeKeyser was involved in the final three goals of the period.
DeKeyser tied it at 2 on his first goal in 25 games, a shot that went off Lightning defenseman Jake Dotchin.
Mrazek stopped Killorn's power-play shot, but DeKeyser put the puck into his own net while attempting to clear it at 16:13.
With DeKeyser off for cross-checking, Drouin made it 4-2 on a shot from the right circle with 1:56 left.
Gourde scored early in the third period, and Green followed with a power-play goal minutes later.
Nielsen and Brown, who stopped a 45-game goal drought, had first-period goals.
"It's been a while," Brown said. "It felt good."
Zetterberg assisted on DeKeyser's goal for his 900th NHL point, coming in his 995th game.
"I've got to give credit to all the players I've played with," Zetterberg said. "I say thanks to them."
Tampa Bay C Steven Stamkos, out since having right knee surgery in November, has been upgraded to day to day. ... The Red Wings announced that C Luke Glendening will miss the rest of the season with a broken ankle/foot. ... Lightning C Tyler Johnson (lower-body injury, 10 games) has resumed skating with the team in practice. ... Red Wings RW Anthony Mantha left with an upper-body injury after fighting Tampa Bay D Luke Witkowski in the first. ... Victor Hedman had an assist and set a Tampa Bay record for defensemen points with 66.
Red Wings: Host Toronto Saturday night.
Lightning: Play the third of a four-game homestand Saturday night against Montreal.