The Sharks (43-24-9) remained six points behind the first-place Calgary Flames and five points ahead of the Vegas Golden Knights. The Flames lost 3-0 at home to the Los Angeles Kings. The Golden Knights lost 3-1 at the St. Louis Blues.
It is the first time San Jose has lost six games in a row (0-5-1) since March 16-25, 2017 (0-6-0).
"We got to fix it," forward Logan Couture said. "There's certain things we need to do better. As a whole, I think our compete and 1-on-1 battles and all that need to go way up.
"It's frustrating to lose six in a row. We're too good of a team to go on a slide like this. These losses at home are not good, especially this one tonight. I thought we'd come with a better effort."
WATCH: [All Red Wings vs. Sharks highlights]
Evander Kane and Tomas Hertl scored in the third period, and Martin Jones made 20 saves for San Jose, which has clinched a berth in the Stanley Cup Playoffs.
"I didn't think we had great energy until the third period," Sharks coach Peter DeBoer said. "I thought we had desperation in the third, but we need it for 60 minutes."
Dylan Larkin, Andreas Athanasiou and Christoffer Ehn scored, and Jonathan Bernier made 39 saves for the Red Wings (28-38-10), who are 4-1-0 in their past five games but have been eliminated from playoff contention.
"We're here to battle," Larkin said. "We want to play for each other and we want to play for next year, and our leaders make sure we're ready every game. So guys have opportunities in front of them, and the opportunity right now is to prove themselves in this league, so these guys coming in now are doing a great job battling and playing hard for us."