Draisaitl was playing in his third game since returning from an undisclosed injury that caused him to miss four games.
Jeff Skinner had a goal and an assist, and Evan Bouchard had two assists for the Oilers (44-26-5), who have won three straight. Calvin Pickard made 27 saves.
Edmonton remained two points behind the Los Angeles Kings for second in the Pacific Division. The Kings defeated the Utah Hockey Club 4-2 on Thursday.
Jack Thompson and Tyler Toffoli scored for the Sharks (20-45-10), who have lost four straight (0-3-1). Mario Ferraro had two assists, and Georgi Romanov made 35 saves.
Connor Brown gave the Oilers a 1-0 lead at 6:22 of the first period. Brown took a pass from Skinner in the neutral zone, skated between two Sharks defenders as he crossed the blue line, and beat Romanov over his glove on a breakaway.
Thompson tied the game 1-1 at 8:10 with a one-timer from the top of the right circle off a pass from Alexander Wennberg from below the goal line.
Viktor Arvidsson put the Oilers back in front 2-1 with a power-play goal at 2:59 of the second period. Draisaitl passed the puck from the right face-off dot into the high slot, where Arvidsson scored with a one-time over the blocker of Romanov.
Draisaitl played just two more shifts following the goal.
Toffoli tied the game 2-2 at 8:48. Macklin Celebrini sent a spinning pass from the right point down to Ferraro, who then sent a backhand feed to Toffoli for a one-timer from the left hash marks.
Skinner responded for the Oilers to make it 3-2 at 14:57. He deflected Bouchard’s wrist shot from the point past Romanov’s blocker.