The Pacific Division-leading Sharks have lost six of eight.
"We were much happier with the effort," San Jose coach Todd McLellan said. "But it is still a loss and we can't get caught up in satisfaction points."
San Jose's Antti Niemi gave up a goal on the second shot he faced and finished with 25 saves.
The Red Wings snapped a five-game losing streak against San Jose in the regular season, beating a team that has eliminated them in the second round in each of the past two postseasons.
"We have a lot of rivals, but that's the one we seem to play a lot in the playoffs," Zetterberg said. "So, you want to win each game against them."
As Sharks captain Joe Thornton was leaving the arena, someone said he'd see him again in Detroit for the playoffs.
"Absolutely," Thornton said with a beaming smile.
Detroit got off to a good start against the Sharks, getting goals from Zetterberg 6:30 into the game and Miller midway through the second, but it wasn't easy to beat them as usual.
Couture was credited for a goal after video review that bounced off the top of the net and appeared to be whacked into the net by Detroit's Justin Abdelkader on a power play with 5:27 left in the second period.
Miller's centering pass set up Helm for a shot from the slot in the third. Later in the period, Marleau finished off a goal-mouth scramble by stuffing the puck past MacDonald.
"I thought we had them on their heels a lot," Thornton said. "If we play like that, we'll be fine. It felt like we had a lot more chances, but obviously they won."
"You're real proud that they sacrifice themselves, but then you're worried about their health," McLellan said.
As much as the Red Wings count on stars such as Zetterberg, its third and fourth-line forwards -- and third-string goalie -- have helped them extend their streak at home.
"That's our secret," Zetterberg said.
The NHL's second-longest winning streak at home this season is eight, shared by Calgary and Colorado. The second-longest active streak at home is five, shared by St. Louis and Phoenix. ... In the shootout's seven-season era, the previous mark for the longest home winning streak was 14 by Boston during the 2008-09 season. ... Detroit's next home game is Thursday night against Vancouver. ... The Sharks beat Detroit 5-2 in their previous meeting and won 4-2 at Joe Louis Arena on Oct. 28.
Copyright by STATS LLC and The Associated Press
Arena: Joe Louis Arena Location: Detroit, Michigan
Referees: Marc Joannette, Stephen Walkom Linesmen: Scott Driscoll, Steve Miller
Attendance: 20,066 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Henrik Zetterberg (13)
Assists: Jonathan Ericsson, Valtteri Filppula
Drew Miller (12)
Assist: Justin Abdelkader
Logan Couture (25)
(Power Play) Assists: Joe Thornton, Joe Pavelski