Alex Iafallo shot into an empty net at 19:35 for the 4-2 final.
Kaliyev gave the Kings a 1-0 lead at 10:04 of the first period, scoring on a quick shot near the right post after Byfield passed him the puck off a rebound in front.
"I was going to shoot, and then I saw 'Arty' just winding up as he always is," Byfield said. "Doesn't matter where you are, he's always winding up for a one-timer, so I saw him in just a perfect spot."
Zegras tied it 1-1 at 3:34 of the second, scoring on a wrist shot from the right circle on a power play. It was his 58th point (22 goals, 36 assists), passing Bobby Ryan (57 in 2008-09) for the most by a rookie in Ducks history.
"I think individual records come from good teams, and I can't score out there by myself," Zegras said. "I played with a lot of good players since I've been here. Some are still here, some are gone, so I think it's a compliment to them. But it doesn't mean a whole lot to me, to be completely honest."
Getzlaf, who sent the cross-ice pass to Zegras, will play his final NHL game against the St. Louis Blues on Sunday.
"Usually when you see a guy retire, he's been pushed down the lineup," Eakins said. "Ryan Getzlaf is going to retire our No. 1 center. There's nobody close to him right now, and that's quite remarkable."
Gerry Mayhew put Anaheim ahead 2-1 at 9:06 of the second on a miscue by Quick. Mayhew chipped the puck in on goal from the neutral zone, and Quick had the puck bounce over his stick as he was attempting to clear it away.
"With 'Quickie's' play for us, maybe it was better that it went in that way than a real good play because the guys buckled down and wanted to play for him," McLellan said. "So it's a sign of a good team and guys playing for one another."