Logan Couture cut it to 4-3 at 8:58 when he scored on a rebound before Karlsson tied it 4-4 with a wrist shot from the left circle at 11:31.
Suter made it 6-4 at 16:23, and Kubalik scored an empty-net goal at 18:45 for the 7-4 final.
"I just think it's important to find a way to win a game," Red Wings coach Derek Lalonde said. "I challenged the guys a little bit, and we really flipped that second period. We started winning those battles, flipped the game, took the lead. Pretty proud of the guys at 4-4, our game was fine. Unfortunately, just two face-off goals hit the back of the net.
"They hung in there and found a way to get a win on the road against a pretty good team, so this is a good win for us."
NOTES: It was Karlsson's ninth multipoint game, and his second four-point game this season; he had three goals and one assist in a 6-5 shootout loss to the Anaheim Ducks on Nov. 1. … Detroit associate coach Bob Boughner returned to San Jose for the first time since he was fired as Sharks coach July 1 after three seasons (67-85-23).