The Ducks went ahead 4-3 on Chris Wagner's first career Stanley Cup Playoff goal at 9:28 of the second, then Gibson made tough saves against Leon Draisaitl, Pat Maroon, Ryan Nugent-Hopkins, Milan Lucic and Andrej Sekera before the period was over to preserve the one-goal lead.
"It got us through the toughest period of the hockey game for us," Ducks coach Randy Carlyle said of Gibson's performance. "We were able to get into the intermission and regroup, then play more of the type of game that's required."
The Ducks started quickly, getting a breakaway goal from Rickard Rakell 25 seconds into the game for the fastest opening goal in Anaheim playoff history.
Silfverberg scored his first of the game at 5:33 to make it 2-0, and Ryan Getzlaf put the Ducks ahead 3-0 at 11:51.
Maroon cut the Anaheim lead to 3-1 when he scored with 39.5 seconds remaining in the first, and Anton Slepyshev got Edmonton within 3-2 when he scored at 1:28.
Forty-eight seconds after McDavid tied the game, Wagner put the Ducks in front to stay when he scored with a shot from near the right boards, a changeup that went in off the blocker of goalie Cam Talbot, who allowed six goals on 28 shots.
Silfverberg scored his second of the game at 4:56 of the third period to make it 5-3. The goal was upheld by video review after Edmonton coach Todd McLellan challenged it, claiming Silfverberg was offside on the play.
Kesler scored at 10:38 to make it 6-3.