Celebrini has 17 points (six goals, 11 assists) during his streak, and 60 points (21 goals, 39 assists) through 39 games this season.
Alexander Wennberg had two assists, and Yaroslav Askarov made 38 saves for the Sharks (19-17-3), who have won two in a row.
Troy Terry had two goals and an assist, Cutter Gauthier had a goal and an assist, and Pavel Mintyukov also scored for the Ducks (21-16-2), who have lost three in a row to match their longest skid of the season.
Lukas Dostal allowed four goals on nine shots before being replaced in the second period by Petr Mrazek, who made three saves in relief.
Wennberg spun away from Anaheim defenseman Drew Helleson along the wall and centered a puck to Mario Ferraro, who had beaten Ducks forward Mikael Granlund down the ice. Ferraro redirected the puck into the net for his 100th NHL point and a 1-0 lead at 10:43 of the first period.
Askarov was indecisive with the puck behind his net, and Nikita Nesterenko stole it from him before getting it out front to Terry, who slid the puck into an open net to tie it 1-1 at 15:02.
Celebrini put San Jose back up 2-1 at 19:12. Wennberg floated a saucer pass to Celebrini in the slot, where he beat Dostal with a snap shot short side.
Igor Chernyshov, who scored his first NHL goal in a 6-3 win at the Vancouver Canucks on Saturday, scored again when he received a pass in front of the Anaheim net after a turnover and he pulled the puck to his backhand before scoring from in close to stretch the lead to 3-1 at 6:30 of the second period.
William Eklund made it 4-1 at 12:17. Celebrini stole the puck from Helleson and skated behind the net before sending a pass to Eklund in the left circle. Eklund then snapped a quick shot far side to chase Dostal from the game.
Gauthier cut it to 4-2 at 16:26 when he redirected a shot by Terry into the net from in front of the crease.
Mintyukov brought Anaheim to within 4-3 at 3:07 of the third period. Gauthier skated into the offensive zone and found Mintyukov in the slot, where he beat Askarov glove side with a wrist shot.
Zack Ostapchuk pushed the lead to 5-3 at 13:47, tipping Vincent Iorio's slap shot from the right point past Mrazek. It was his first goal since Jan. 19, 2025.
Anaheim pulled Mrazek with just under five minutes left and Terry scored from the side of the net during the 6-on-5 to cut it to 5-4 at 15:58.
After going on a power play with 3:09 left, the Ducks pulled Mrazek for the two-man advantage, but couldn't get the tying goal.