Getzlaf made it 3-1 with 3:16 remaining, Fowler scored to get the Ducks within 3-2 with 2:41 left, and Rakell tied it 3-3 with 15 seconds remaining when he backhanded a loose puck past goalie Cam Talbot.
Rakell's goal was upheld after the NHL Situation Room and the referee determined that the actions of Edmonton defenseman Darnell Nurse caused Anaheim forward Ryan Kesler to contact Talbot before the puck crossed the goal line.
"It wasn't a good birthday to start, but it was a good ending," said Rakell, who turned 24 Friday.
Connor McDavid had a goal and an assist, Leon Draisaitl and Drake Caggiula scored, and Talbot made 60 saves, an Edmonton record.
"We have to come back with a game that's that much better," Oilers coach Todd McLellan said. "We can do that. We believed we can play with this team from Day One."
Draisaitl put the Oilers up 1-0 when he scored 15 seconds into the second period. McDavid made it 2-0 when he batted the puck out of midair to score on a 5-on-3 power play at 2:55. Then, on a 3-on-1, McDavid got an assist on Caggiula's goal that made it 3-0 at 12:28 for his first multipoint game in the playoffs after he had 30 during the regular season.
Perry and Jakob Silfverberg each had two assists, and Gibson made 35 saves.
Nick Ritchie beat Talbot with a deflection at 10:45 of the second period, but referee Francois St-Laurent ruled he did so with a high stick and waved off the apparent goal. Video review confirmed Ritchie's stick was above the crossbar when it contacted the puck.
Edmonton defenseman Andrej Sekera left the game at 5:51 of the first period after he was injured on a hit by Getzlaf in the neutral zone.
Getzlaf missed the net on a penalty shot at 9:12 of the first after Milan Lucic was called for holding him on a breakaway.
