Tomas Hertl scored, and James Reimer made 22 saves for the Sharks (29-31-9), who have lost four straight (0-3-1).
"That's one of our best, most solid games in a long time, and a little bit the story of our year," San Jose coach Bob Boughner said. "We had so many chances. Smith plays great and you can't get that second goal that you need and change the whole face of the game. And that's a team that takes advantage of things. ... But I will say, looking at the game itself, we did so many great things, and that's encouraging. That was our best game we've played in a long time."
Hertl put the Sharks ahead 1-0 at 15:32 of the first period on a power play. Burns set the play up with a cross-ice pass, and Hertl scored from the right face-off circle on a slap shot from one knee.
Nugent-Hopkins tied it 1-1 at 11:56 of the third period with a shorthanded goal.
"When you wake up [Wednesday], it will be nice to at least have gotten one point," Reimer said. "I thought we battled hard, we played really well. Probably one of our better [games] in the last week. It just came down to OT. We had some looks and they had some looks and they ended up getting one extra."
NOTES: McDavid extended his goal streak to five games (six goals). ... Forward John Leonard left in the second period after being hit in the leg with the puck, and forward Jonah Gadjovich left in the third period after being hit in the hand with the puck. Boughner did not have an update on either player. … Oilers forward Zach Hyman had an assist and has seven points (three goals, four assists) in his past seven games. … San Jose forward Timo Meier had an assist and has 10 points (six goals, four assists) in his past eight games. … Hertl has nine points (two goals, seven assists) in his past seven games.