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The Oilers visit the Florida Panthers on Saturday at 12:00 p.m. MDT. The game can be seen on Sportsnet West and heard on 630 CHED and the Oilers Radio Network.
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Connor McDavid registered a pair of helpers, putting him up to 53 assists and 86 points in 2017-18.
Oscar Klefbom - who will eventually be shut down after a looming shoulder procedure - tallied one goal and one assist in 19:46 of ice time.
"I think I've played many games better than I did tonight but the puck went in," said Klefbom. "I'd rather score no goal and win a game. It's a tough one."
Drake Caggiula and Ryan Nugent-Hopkins rounded out the scoring, while Al Montoya made 36 saves on 40 shots - good for a .900 save percentage.
"I thought we handled the game pretty well and controlled it," said Montoya. "They battled back and got the extra bounce at the end."
The home side gained three separate regulation leads against San Jose, ultimately failing to maintain each of them as the Sharks stayed afloat through 60 minutes then pounced in overtime.
"We turned a few pucks over, which allowed them to get back into it," said Oilers Head Coach Todd McLellan. "When our backup goaltender gives us a performance like that, we should be able to find a way to close it off."
It didn't take long for the Oilers to get their chances, as Edmonton jumped out with energy early in the game.
McDavid sprung Nugent-Hopkins on a breakaway just over a minute in but No. 93's wrist shot was stopped by San Jose netminder Martin Jones.
Leon Draisaitl then found himself at the side of the net with loads of time, firing a quick shot that Jones kicked out with his pad.
The pressure trickled down to the Oilers fourth line, who opened the scoring.
Zack Kassian held the puck behind the Sharks' net, sucking two defenders to him. As defenceman Brenden Dillon approached, Kassian threaded a behind-the-back pass through Dillon's skates right on Caggiula's tape. Caggiula buried his ninth of the season and 15th point 2:39 in.