Ryan Getzlaf and Patrick Eaves scored for the Ducks, who have lost two in a row following a five-game winning streak. John Gibson stopped 34 shots.
Anaheim had the best early chance six minutes in, but Talbot made a huge glove save on a point-blank shot by Corey Perry.
Edmonton finally got on the scoreboard with 49 seconds left in the opening period as Patrick Maroon’s nice individual effort set up McDavid’s 29th goal. It gave the second-year start his league-leading 92nd point and extended his points streak to 10 games.
The Ducks pulled even on the power play early in the second when Getzlaf beat a screened Talbot with a blast from the point for his 15th.
Anaheim defenseman Sami Vatanen left the game in the second with an upper-body injury and did not return.
Ducks forward Ryan Kesler had a wide-open net to shoot for four minutes into the third, but rang it off the crossbar.
Anaheim took a 2-1 lead nine minutes into the third on the power play, as the Oilers got caught running around and Antoine Vermette was left alone in front to dish it to Eaves at the side of the net for his 29th.
Edmonton tied it back up with a power-play goal of its own with 1:58 remaining when Lucic scored from in tight on the rebound of Draisaitl’s shot, whose assist also gave him a 10-game point streak.
NOTES: Gibson, who had been sidelined with a lower-body injury, made his first start since March 10. … It was Edmonton coach Todd McLellan’s 700th game.
Ducks: At Calgary on Sunday night.
Oilers: At Los Angeles to start a three-game trip.