"The way hockey is sometimes, you get on that roll," Sharks center Joe Thornton said. "And this year the injury bug kind of hit us and it kind of hurt us. But no excuses. They played a great series, and hats off to them."
Draisaitl scored 54 seconds into the second period to put the Oilers ahead 1-0. He got behind the Sharks defense to take a stretch pass from Adam Larsson, fended off defenseman Justin Braun, and beat Jones.
Less than a minute later, Slepyshev scored unassisted on a breakaway when he shot past Jones' blocker to make it 2-0 at 1:50.
Marleau scored from the left of the Oilers net off a pass from Logan Couture through the slot at 12:12 of the third period to get the Sharks within 2-1. It was his third goal of the series, 68th in the NHL playoffs in his career.
Edmonton killed a San Jose power play after being penalized for too many men on the ice with 4:57 remaining. Sharks forward Joe Pavelski beat Talbot with a backhand but hit the crossbar with 3:46 left.
"It was definitely nerve-wracking, but I think we stayed composed and disciplined in our game, especially in our penalty kill," Oilers forward Milan Lucic said. "[Talbot] made some huge saves for us. They got some tips and some bounces in front, and we were able to get some saves and not allow some second opportunities.
"Definitely made it a little bit harder on ourselves, but you knew they were going to push and fight for their lives, but at the end of the day, this one feels good."
Edmonton defenseman Oscar Klefbom did not play in the third period because of an illness. Several Oilers, including Draisaitl, have had the flu.