Gauthier gave Anaheim a 5-4 lead at 15:08, pouncing on a rebound and burying it from the bottom of the left face-off circle into an open net for his second goal of the game. Ryan Poehling then scored an empty-net goal at 18:50 to secure the 6-4 final.
Alex Killorn had a goal and two assists, and Poehling scored his first two playoff goals for the Ducks, who are the No. 3 seed from the Pacific. Jackson LaCombe had three assists, Gauthier also had an assist, and Lukas Dostal made 33 saves for his first career playoff win.
Leon Draisaitl had a goal and an assist, and Connor Murphy and Zach Hyman scored for the Oilers, who are the No. 2 seed from the Pacific Division. Connor Ingram made 22 saves.
The Ducks evened the best-of-7 series 1-1. Game 3 will be at Honda Center in Anaheim on Friday (10 p.m. ET; TNT, truTV, HBO Max, SN, CBC, TVAS, KCOP-13, Victory+).
Draisaitl put the Oilers up 1-0 at 8:58 of the first period. He settled a rebound below the right circle and put a sharp-angle wrist shot on net that deflected in off the right skate of Ducks defenseman Drew Helleson.
Helleson was in the lineup in place of Radko Gudas, who reaggravated a lower-body injury that sidelined him for eight of Anaheim's final 10 regular-season games. Helleson was minus-1 and had one shot on goal in 7:52 of ice time in his playoff debut.
Gauthier tied it 1-1 with a power-play goal at 12:48 when he used Beckett Sennecke as a screen and beat Ingram with a long-distance wrist shot to the blocker side for his first playoff goal.
Jacob Trouba put the Ducks up 2-1 at 2:44 of the second period with a wrist shot from the right point that went under Ingram's right arm through traffic.
Killorn made it 3-1 while on the power play at 5:35 after his attempted pass through the slot deflected off the stick of Oilers defenseman Evan Bouchard and then rebounded off Ingram. Killorn then lifted the puck over Ingram's outstretched glove from in tight.
Murphy cut the deficit to 3-2 with his first playoff goal at 11:46, taking a pass from Draisaitl and burying a slap shot past a screened Dostal to the glove side.
Poehling scored his first career playoff goal while short-handed to push the lead to 4-2 at 15:50. He tipped a Killorn pass from in front after Edmonton captain Connor McDavid gave the puck away in the defensive zone.
Hyman brought the Oilers to within 4-3 at 17:48. Mattias Ekholm put a slap shot on net from the left point, and Hyman deflected the puck in off the right post from the slot.
Josh Samanski, who made his playoff debut, tied it 4-4 at 13:51 of the third period. Jack Roslovic sent a pass from behind the net into the left circle, where Samanski snapped a shot in off Dostal's glove. Samanski was in the lineup in place of Adam Henrique, who left Game 1 with a lower-body injury late in the first period.
McDavid left for the dressing room early the second period with an apparent right ankle injury during a collision involving Ekholm and Ducks forward Ian Moore, but returned to the ice soon after.
