Draisaitl cut the deficit to 3-1 at 1:34 of the third. Bouchard's one timer from the point deflected off Sharks defenseman Dmitry Orlov in the slot and through the pads of Askarov before Draisaitl poked the loose puck over the goal line as it sat in the crease.
McDavid brought the Oilers to within 3-2 at 16:55, scoring with a wrist shot from the left circle.
Both McDavid's and Bouchard's goals came while Ingram was pulled for an extra attacker.
“I think we went into defense mode a bit too early,” San Jose defenseman Timothy Liljegren said. “We got back on our heels a little bit. I thought they had a good push and we sat back a little bit too much and they scored.
“Edmonton is a very good team, they showed that the last several years. It’s not an easy game. I thought we played well for 40 minutes. There are always things we can do better, but I thought in the third we sat back too much and let them take over the game.”
Graf opened the scoring just 26 seconds into the first period. Will Smith sent a cross-ice pass to Graf in the left face-off circle, where he put a wrist shot into an open net.
“I thought we played pretty well for 56 minutes, or whatever it was,” Graf said. “We just have to try to be better in all facets of the game. They’re going to get their chances and it’s on us to try to limit them as much as we can and try to keep them to the outside, and we did a pretty good job until the end there.”
Gaudette made it 2-0 at 1:35. William Eklund forced a turnover in the neutral zone and fed the puck to Gaudette, who skated in on a breakaway and lifted a backhander over Ingram's right pad.
Misa extended the lead to 3-0 at 11:40 after his snap shot from the right circle rebounded off Ingram and then deflected in off Bouchard.
Barclay Goodrow appeared to put the Sharks up 4-0 at 6:42 of the second period when he scored into an open net, but officials waved it off because of goaltender interference against Zack Ostapchuk.
NOTES: The Oilers overcame a three-goal deficit in the third period for the first time since Nov. 26, 2022 (4-3 win at the New York Rangers). ... Bouchard has 11 points (four goals, seven assists) in a four-game streak. ... McDavid (four goals, five assists) and Draisaitl (one goal, nine assists) each have three-game point streaks. ... McDavid became the fifth player in NHL history to record 10 career 60-assist seasons, joining Wayne Gretzky (17), Paul Coffey (11), Ray Bourque (10) and Adam Oates (10). ... Sharks forward Macklin Celebrini extended his point streak to three games (three goals, four assists).