The deciding goal was netted by Larsson, who skated in behind the Ducks goal and threw it in front with 4:40 to go. The puck ricocheted off Josh Manson in front and in to put the Oilers up 4-3.
"Sometimes it's probably better to shoot it and put it on net rather than overthink it and that's what I did," said Larsson.
Prior to Larsson's marker, the teams traded goals rapidly through the midway point of the third period.
First, Letestu put home his second goal of the game. Always opportunistic, he was perched at the side of the net and pounced on the puck before rifling it past Gibson to give the Oilers the lead.
"I've had a few in that spot, it's kind of just my area on the power play," Letestu stated. "We had lucky bounces tonight. One was a rebound, Leon found a way to get one through to me (on the other), it's my job to get it on net and get it by the goalie."
1:40 later, the Oilers struck again to take a two-goal lead. Larsson wired a wrist shot in the slot by Gibson for his first of the night.
And then the Ducks scored two in 1:25.
Just over a minute after the Larsson goal, Anaheim got that one back. The Ducks won the draw and Patrick Eaves pounced on a rebound in front, putting the puck by Cam Talbot to make it a 3-2 game.
Andrew Cogliano's shot from the right circle was stopped by Talbot but Silfverberg batted the rebound out of the air past Talbot to tie the game up. The Oilers called a coach's challenge for goaltender interference but it was ruled a good goal and a 3-3 game.
"That was an evenly played game by two good hockey clubs," said Oilers head coach Todd McLellan following the game. "It could have went either way. It's the second round, it gets ramped up a little more. Shot blocking goes up, line changes become important. The deeper you go, the more intense those moments become."
Leon Draisaitl's only goal was the empty netter but he put in an outstanding effort with a goal and three assists for four points plus 6-for-7 in the faceoff dot in a game where the Ducks won 57% of the draws.
"They, being Connor and Leon, push and pull each other and are happy for each other," McLellan began. "There's so much attention put on 97 right now, there's such a focus that others have to pick up the slack. Sometimes there's ice available and in my opinion, Leon took advantage of it tonight."
After a scoreless but very physical first period where the two teams traded power plays, Anaheim scored on the man advantage 37 seconds into the second to take a 1-0 lead. Ryan Getzlaf wired a shot from the right circle past Talbot for the marker.
Less than five minutes into the middle frame, the Ducks continued to be physical with the Oilers but this time it cost them. Nick Ritchie drove his way to the net, fending off Oscar Klefbom while doing it and received two minutes for holding as a result. Oilers went on the power play for the third time.
With 55 seconds left in the Ritchie penalty, Hampus Lindholm got two for high-sticking Leon Draisaitl. The Oilers then went on a two-man advantage where they capitalized to tie the game.
After bouncing off skates in front, a loose puck rolled over to Mark Letestu who quickly fired it high above an outstretched Gibson to tie the game up at 1-1 with 13:38 to go in the second.
The Oilers started to answer the Ducks physical play with some of their own but like Anaheim, it resulted in some time in the box. Slepyshev bowled Gibson over after the Ducks goaltender denied the Russian on a partial breakaway and served two in the bin as a result.
Anaheim did not score on that power play, but Jakob Silfverberg nailed a shot off the post - one of many posts that were hit by both teams in this one.
With the game knotted at 1-1, shots on goal were 20-20 after two periods; 10-9 for Anaheim in the first and 11-10 Oilers in the second.
Anaheim started the third period on a roll with five straight shots in the opening two minutes but the Oilers started to steal back some of that Ducks momentum.
As he broke for the net, McDavid was held up by Silfverberg giving the Oilers a man advantage early in the period, setting up Letestu's second of the night.