Askarov, who was traded to San Jose by the Nashville Predators on Aug. 23, also had his first NHL assist.
"That was nice," Askarov said. "[It's] always fun to win."
Anze Kopitar had a goal and an assist, and Brandt Clarke also scored for the Kings (11-8-3), who have lost four of their past six games. David Rittich made 14 saves.
"One thing people have to understand is, you shouldn't disrespect this team," Los Angeles coach Jim Hiller said. "That's not a team trying to tank. That is a good hockey team. Strong players. We played them three times; they beat us twice."
Celebrini put the Sharks ahead 3-2 at 1:03 of the third period on a shot near the left boards.
"We wanted to set the tone at the start of the third and get on them right away," Celebrini said. "I was happy that went in."
Timothy Liljegren extended it to 4-2 at 3:14 when he took a pass from Smith and scored on a one-timer from the top of the right circle.
Celebrini scored his second goal of the period on the power play to make it 5-2 at 3:43, a one-timer from the right circle.