Lucas Raymond scored the only goal in the shootout.
Emmitt Finnie had a goal and an assist for Detroit (3-3-2), which finished a stretch of playing seven of their first eight games at home. John Gibson made 31 saves.
Macklin Celebrini had a goal and two assists, and Ivar Stenberg had a goal and an assist for San Jose (4-3-1), which had been 4-0 in overtime and shootouts. Former Red Wings goalie Alex Nedeljkovic made 24 saves.
With Gibson on the bench for an extra attacker, DeBrincat put in a rebound to make it 3-3 at 18:27.
Andrew Copp was called for holding Celebrini at 2:32 of overtime, but the Red Wings killed the power play.
San Jose nearly took the lead midway through the first period, but Gibson made a kick save while sprawled on the ice to rob Celebrini.
Justin Faulk gave the Red Wings a 1-0 lead at 12:47, scoring a power-play goal with a point shot through traffic.
Dmitry Orlov tied the game 1-1 with a nearly identical goal at 17:59, beating Gibson from the point for a power-play goal.
Celebrini made it 2-1 at 4:55 of the second period. Michael Kesslering intercepted William Wallinder’s clearing attempt and passed to Will Smith, who got the puck to Celebrini in the high slot on a touch pass for his third goal.
San Jose took a 3-1 lead at 2:48 of the third period with their second power-play goal. A quick passing play ended with the puck on Stenberg’s stick and he put a shot under the crossbar for his second career goal.
Finnie got Detroit within 3-2 at 5:00, finishing a rush by putting in Michael Brandsegg-Nygard’s pass at the far post.
