Radek Faksa and Ryan Suter also scored in the third period, and Robert Thomas and Jordan Kyrou each had two assists for the Blues (2-0-0). Joel Hofer made 25 saves.
"Considering how we played in the first, I thought we had played pretty clinical," St. Louis coach Drew Bannister said. "There were a lot of great things. We got away from forechecking and playing direct. Then in the third we went back to what worked well for us in the first."
Tyler Toffoli had a goal and an assist, and Blackwood made 35 saves for the Sharks (0-1-0).
"Thought [Celebrini] was really good," San Jose coach Ryan Warsofsky said. "Obviously, points are one thing. [There are] some things he needs to learn without the puck, him and [Will Smith], but I thought they were both solid in their debuts."
Celebrini, who was selected with the No. 1 pick in the 2024 NHL Draft, gave San Jose a 1-0 lead at 7:01 of the first period. He attempted to send a spinning backhand pass to William Eklund in the slot, but the puck deflected in off the skate of Blues defenseman Matthew Kessel.
"Eklund [told me I scored]. I was like, 'Nice goal,' and he was just like, 'I didn't score either,'" Celebrini said. "I thought he was just super excited that he scored, but I guess he was happy for me.
“I think just the whole process going into it, all my teammates and going through it with 'Smitty' was really cool. Just all of those memories, those plays, first shift, all that. The warmup, rookie lap. I tried to soak up as much as I could.”