O'Reilly put St. Louis ahead 6-5 at 3:20, but Couture tied it 6-6 at 6:31.
Scandella scored his second of the game to give the Blues a 7-6 lead at 7:14.
"It's been a long time," Scandella said regarding his previous two-goal game. "Probably in the American Hockey League. It felt unbelievable."
San Jose's Devan Dubnyk allowed seven goals on 31 shots.
"I haven't been in a game like that in a long, long time, so it was a strange one. Disappointing," Dubnyk said. "I thought that we played really well as a group, and I just wanted to be able to come up with something there when the guys keep coming back and tie at 5-5, 6-5 and 6-6. You want to be able to knock one down for them, so [it stinks]. Just got to forget about it as best you can and get ready for the next game."
Meier scored 17 seconds into the game when his shot went in off defenseman Torey Krug's elbow to give the Sharks a 1-0 lead.
Scandella scored his first goal with the Blues to tie it 1-1 at 6:08 of the first period. He was acquired in a trade from the Montreal Canadiens on Feb. 18, 2020.
Kane scored on the power play at 10:11 to give San Jose a 2-1 lead.
Sammy Blais scored at 3:34 of the second period to tie it 2-2.
Meier scored his second of the game on a power play at 6:43 to put the Sharks ahead 3-2, but Brayden Schenn scored 45 seconds later to tie it 3-3 at 7:28.
Kane scored his second of the night to make it 4-3 at 10:34 and chase Binnington from the game.
Binnington was assessed a minor penalty for unsportsmanlike conduct after he shoved Radim Simek in front of the San Jose bench, put his blocker in Erik Karlsson's face and confronted Dubnyk on his way off the ice.
The Blues tied it a fourth time, 4-4, when Sanford scored at 18:16.
NOTES: The Blues and Sharks tied the NHL record for most tying goals in a regular-season game (six). It happened three other times in the past 20 years (Vancouver Canucks vs. Colorado Avalanche, Nov. 2, 2018; Detroit Red Wings vs. San Jose Sharks, Nov. 26, 2005; and Colorado vs. Montreal Canadiens, Dec. 6, 2002). ... Meier's goal at 0:17 was the second time this season the Sharks scored in the first 20 seconds of a game (Couture at 0:11 on Feb. 6). San Jose is the only NHL team to do it twice in 2020-21. ... St. Louis, already missing seven players because of injury, took another hit when forward Jacob de la Rose left in the first period with a lower-body injury. There was no update after the game. ... The Blues are 8-1-1 in their past 10 games against the Sharks, including the Stanley Cup Playoffs.