A replay review followed to determine whether Talbot was interfered with in the crease by Ryan Kesler, but the call on the ice stood, igniting the Honda Center crowd yet again.
Rakell, who turned 24 today said, "It wasn't a good birthday to start, but it was a good ending."
The Ducks actually outshot the Oilers 14-9 in the first overtime (giving Anaheim 58 for the night), but Edmonton had the majority of the quality chances in the session. Anaheim also wasn't able to cash in a late power play after the Oilers were whistled for too many men on the ice.
But the second overtime turned the Ducks back toward the net where they pulled off their amazing comeback in regulation, and they did it again 6:57 into the second extra session thanks to the magic of Getzlaf and Perry.
"When you're playing in a playoff series, it's about sticking with it and staying with the things you're doing," Getzlaf said. "We had a lot of looks early that we didn't bury and obviously they did. We had some opportunities at the end and it was great to get that win."
The Ducks were seemingly undone in an exasperating second period in which they gave up three unanswered goals to fall into that 3-0 hole that lasted late into regulation.
"I don't think I heard once on the bench any frustration or anything," Perry said. "It was a matter of going out for the next shift."
Anaheim had a number of opportunities in the first period - including two power plays and a Getzlaf penalty shot - but came up empty. Instead, it was the Oilers who struck first, just 15 seconds into the second period, when a Leon Draisaitl bad-angle shot was initially stopped but then kicked over the stripe by Gibson.
Back-to-back penalties by Nick Ritchie (charging) and Fowler (hooking) opened the door to a 5-on-3 in which the Oilers made Anaheim pay when Connor McDavid batted in an airborne puck past a sprawled Gibson.
Ritchie appeared to get the Ducks within a goal just past the midway point of the period, but officials quickly ruled he tipped the puck with a high stick and confirmed it via replay review. He later endured an extended absence when he engaged in a fight off a draw with Edmonton's Zack Kassian, and they were each handed 10-minute misconducts on top of their majors.
Edmonton extended their lead to 3-0 with 7 1/2 minutes left on the odd-man rush when McDavid fed Caggiula for the one-timer, a seemingly insurmountable deficit until the Ducks pulled off a comeback you truly had to see to believe.
"I don't know if there is a recipe or something you can hang your hat on other than you can't quit believing when you're in any situation," Ducks coach Randy Carlyle said. "Momentum swings in the playoffs are so drastic and they mean so much. When you're able to get one, you start to believe and it sends a different message to the opposition. You get two and you can really get this done.
"We just found a way to will it across the line at the end. It's a great achievement for our players and we should feel good about ourselves, but the next one will be the toughest one in their building."