Milano, one of five players who made their Anaheim debut, drew a tripping penalty on Connor McDavid at 1:09 of overtime and scored on the power play at 2:05.
"We had a set play that didn't work out, but we went with our gut there," Milano said of the game-winner. "Adam] Henrique told me to switch out and he gave me a good pass. I just tapped it in."
***[WATCH: [All Oilers vs. Ducks highlights]*
Henrique had a goal and an assist, and John Gibson made 29 saves for the Ducks (25-30-8), who had lost five straight at home (0-4-1).
Tyler Ennis and Andreas Athanasiou each had a goal and an assist in their debut, McDavid had three assists while centering their line, and Mike Smith made 17 saves for Edmonton (33-22-8), which is tied with the Vancouver Canucks for second place in the Pacific Division, two points behind the Vegas Golden Knights.
"I thought they were great, they made plays all night," McDavid said of Ennis and Athanasiou. "I really liked playing with them."
Athanasiou poked in the puck as it sat in the crease behind Gibson following a save on Ennis to tie it 3-3 at 15:25 of the third period.
"I thought we stuck with our game plan," Henrique said. "We kept battling, kept pushing, even after they tied it up."