Kevin Fiala also scored for the Kings, who won for only the second time in 11 games. David Rittich stopped 22 shots.
Quick made 24 saves in his first game in Los Angeles since being traded by the Kings to the Columbus Blue Jackets on March 1 last season. Quick eventually wound up with Vegas and picked up a third Stanley Cup ring.
The Kings gave Quick a two-minute tribute on their videoboard during the first period.
Chris Kreider scored for the Rangers. New York had a power play for the final 1:39 of the game after Trevor Moore was called for high sticking, but the Kings killeds it off. It was the 25th time in the last 26 chances the Kings have not allowed a goal on the power play.
Quick, who turns 38 on Sunday, backstopped the Kings to their Cup titles in 2012 and 2014. He won the Conn Smythe Trophy as playoff MVP in 2012 after recording three shutouts in 20 starts.
A third-round pick by the Kings in 2005, he holds the franchise records for goalies in games played (743) and shutouts (57).
Four minutes after Kreider tied it, Byfield crashed the net to put the Kings back on top 2-1. Jaret Anderson-Dolan’s backhand went off Quick’s left shoulder and down his back, but didn’t cross the line. After a rush in front of the net, Byfield was there to bury the rebound at 18:13 for his 13th of the season.
Fiala snapped a six-game goal drought with 34.4 seconds remaining in the first period. Moore made a nice pass near the crease to Fiala, who waited for Quick to commit and then fired it into a near-open net after Quick was sprawled on the ice.
Kreider evened it at 14:39 of the second when he redirected Adam Fox’s pinpoint pass into the net and beat Rittich on his short side. Not only was it Kreider’s 21st this season, but it was his 136th road goal with the Rangers, tied for fourth-most in team history.
Alexis Lafrenière took a puck to the face on a shot by the Rangers’ Artemi Panarin with 8:48 remaining in the third period but returned less than two minutes later.
Up next for the Kings: vs. the San José Sharks at Crypto.com Arena on Monday night.