Iafallo scored a power-play goal at 9:19 of OT by converting Victor Arvidsson's feed from behind the net.
“Alex is kind of our unsung hero,” Kings head coach Todd McLellan said. “He cleans up. (Assistant coach) Trent Yawney always says he cleans up a lot of messes. Errors, mistakes, for teammates, he seems to be the cleanup guy. But on the other side of it, he has the ability to score. He can go up and down the lineup, penalty kills, blocks shots.
Adrian Kempe scored twice and Anze Kopitar had a goal and three assists for Los Angeles, which held Oilers captain and NHL scoring leader Connor McDavid scoreless.
Kings goaltender Joonas Korpisalo made 38 saves for the win.
Leon Draisaitl countered with a pair of goals and Evan Bouchard also scored for the Oilers (50-23-9), who ranked second in the Pacific Division this season ahead of third-seeded Kings (47-25-10).
Oilers starter Stuart Skinner stopped 31 shots in his NHL playoff debut.
Edmonton defenseman Vincent Desharnais was penalized in overtime for tripping Blake Lizotte, although Lizotte appeared to step on a broken stick on the ice and fall.
“My initial thought on the play was that the player stepped on the broken stick, but those are the things you know, that happen in the playoffs sometimes,” Oilers head coach Jay Woodcroft said.
The Oilers almost ended it at 1:54 of OT, but officials ruled Ryan McLeod’s shot from the blue line deflected off Derek Ryan’s high stick.
The Oilers will try even the series in Wednesday’s Game 2.
Edmonton also dropped the opener of a first-round series against the Kings last year, but the Oilers took it in seven games to advance.
The Oilers led Monday’s opener 2-0 after the first and second periods before a four-goal third.
Kempe halved the deficit 52 seconds into the third period when the clubs played four aside.
Draisaitl restored Edmonton’s two-goal lead at 8:46 only for Kempe to pull his team within a goal again at 11:23.
With Bouchard serving a high-sticking penalty, and Korpisalo pulled for an extra attacker, Kopitar produced the equalizer with 17 seconds remaining in regulation.
The puck lay in the crease for Kopitar to poke in after Philip Danault’s shot squeezed between Skinner’s pads.
Quinton Byfield fed Kempe following an offensive zone faceoff for the latter to beat Skinner with a shot far side for his second goal of the game.
Korpisalo made the initial save on Draisaitl’s backhand attempt as the big centre skated out from behind the net.
The puck squirted loose in the ensuing goalmouth scramble. Draisaitl skating by again reached back to get a shot away for his second goal.
Kempe cut from the wing to the high slot and put a backhand by Skinner’s glove for his first of the game.
The Oilers killed off a pair of penalties early in a goal-free second period.
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