Detroit, which broke the league's single-season record of 20 on Tuesday, surpassed the 22 wins in a row the Boston Bruins had over two seasons more than eight decades ago.
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The Red Wings won their sixth straight game, all in a homestand at Joe Louis Arena, and have an NHL-high 84 points.
The Pacific Division-leading Sharks have lost six of eight.
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.
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.
Miller's centering pass set up Helm for a shot from the slot in the third. Later, Marleau finished off a goal-mouth scramble by stuffing the puck past MacDonald.