The Sharks will take their 3-1 series lead back home with a chance to advance on Sunday night to the N.H.L.’s conference finals.
Detroit is trying to become the fourth N.H.L. team to win a series after trailing by 3-0.
The veteran defenseman Nicklas Lidstrom scored twice in the first period to help the Red Wings take a three-goal lead that they let slip away.
Logan Couture had a goal 15 seconds after Lidstrom’s second, Dan Boyle scored midway through the middle period to pull San Jose within 3-2, and Dany Heatley tied the score early in the third.
Helm put Detroit back ahead for good, scoring from the left circle off a cross-ice pass from Patrick Eaves, who got the puck off a long rebound after Brian Rafalski’s shot.
“For us it was an overtime game, a game we obviously had to win,” Helm said.
Jimmy Howard made 25 saves for the win. San Jose’s Antti Niemi stopped 26 shots.
The second-round rematch has mirrored last year’s matchup between the teams. San Jose won the first three games by a goal each time, but could not complete the sweep.
Todd Bertuzzi scored first this time 6:22 in, just as he did last year in Game 4, when he gave Detroit a 1-0 lead at 5:40.
The Red Wings went on to win that game, 7-1, before being eliminated in Game 5.
Detroit appeared to be on the way to another blowout win after Lidstrom scored twice in the first period to make the score 3-0, but San Jose refused to get routed.
Couture quieted the crowd at Joe Louis Arena, and Boyle silenced the fired-up fans again when he made the score 3-2 at 13:44 of the second.
Detroit had chances to add to its lead in the second but went 0 for 3 on the power play in the period.
San Jose did not have a power play in the first two periods.
The Sharks got their chance 4:12 into the third, shortly after tying the score, but they did not take advantage.
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