Kapanen took a pass in the slot from Vasily Podkolzin, who was behind the net, and beat Lukas Dostal glove side with a one-timer.
His goal came after Jason Dickinson, who was returning from a lower-body injury that kept him out the final three regular-season games, tied it 3-3 with his second goal at 11:30 of the third. Ducks defenseman Radko Gudas fell to the ice while skating back into the zone, which allowed Mattias Ekholm to skate in uncontested and put a slap shot on Dostal from the left circle. The Ducks goalie made the initial save, but the rebound kicked right out to Dickinson, who buried it into the open net.
Leon Draisaitl had two assists in his return after missing the final 14 games of the regular season with a lower-body injury for the Oilers, who are the No. 2 seed from the Pacific Division. Connor Ingram made 23 saves.
Troy Terry scored twice and added an assist, and Leo Carlsson had a goal and an assist for the Ducks, who are the No. 3 seed from the Pacific. Dostal made 30 saves.
Game 2 of the best-of-7 series will be here on Wednesday (10 p.m. ET; CBC, SN, TVAS2, KCOP-13, TBS, Victory+, HBO MAX).
Dickinson put the Oilers ahead 1-0 at 17:21 of the first. He got behind Ducks defenseman Tyson Hinds, took a lead pass from Jake Walman, and deked Dostal on a breakaway before putting a backhand into an open net.
Kapanen made it 2-0 exactly one minute later at 18:21. He chopped down his own rebound in the low slot before batting the puck in past a diving Dostal near the left post.
Terry cut it to 2-1 just 19 seconds into the second period, getting the rebound of Carlsson's shot in the right circle and scoring past Ingram's outstretched left pad.
Carlsson tied it 2-2 at 4:37, this time tapping in the rebound of a shot from Terry.
Terry then gave Anaheim its first lead of the game, 3-2, on a power play at 14:29. He scored with a wrist shot from the top of the left circle through a screen by Chris Kreider and over Ingram’s right shoulder.
