Nikita Kucherov (one goal, three assists) and Victor Hedman (four assists) each scored four points, and Steven Stamkos had two goals and an assist for the Lightning, who responded from a 6-2 loss to the Pittsburgh Penguins on Tuesday. Andrei Vasilevskiy made 20 saves.
"We could have easily quit on that game, being down multiple goals numerous times, but we didn't give up and we got rewarded for it," Stamkos said. "I don't know to explain it. That was a weird game."
Alex Nedeljkovic made 41 saves in his Red Wings debut after being acquired in a trade with the Carolina Hurricanes on July 22. Moritz Seider had two assists in his NHL debut.
"Obviously when you've got a three-goal lead in the third period, it is really a gut punch to end up with a loss," Detroit coach Jeff Blashill said. "I thought we were going to find a way to finish off that game."
Ross Colton made it 6-4 at 13:43 and Kucherov cut it to 6-5 with a power-play goal at 16:25. Killorn tied it at 17:41.
"There's a bit of a winning pedigree in that locker room, and they've shown that fight before," Cooper said. "After what happened on opening night, it was paramount that we come away from this game with points."
Dylan Larkin gave Detroit a 1-0 lead at 14:00 of the first period, and Bertuzzi scored 18 seconds into the second, stickhandling through his legs to split Hedman and Sergachev to make it 2-0.