Panarin added his team-best 28th goal at 17:11 before Angelo fired home an empty-netter with 2:11 left. It was DeAngelo’s 13th of the season.
Shesterkin made 10 saves in the first, 15 in the second and 17 more in the third. The 24-year-old Russian goaltender has won three straight. He heard chants of “Igor! Igor!” from the Madison Square Garden crowd during the third period.
McKegg scored 2:23 into the first period, rifling the puck past Jonathan Quick from the left faceoff circle. It was McKegg’s third goal of the season and second in three games.
Quick made 37 saves for the Kings, who have dropped five in a row.
Los Angeles (19-33-5) played its third game in the New York area in four nights. It began a four-game trip with a 4-2 loss at Washington, followed by a 5-3 defeat against the Islanders in Brooklyn on Thursday. The Kings were then blanked 3-0 by the Devils on Saturday.
The Kings have the worst record in the Western Conference and played their league-high 33rd road game. Los Angeles has only eight wins away from Staples Center.
NOTES: The Rangers scratched defenseman Brendan Smtih and goaltender Alexandar Georgiev. … The Kings scratched defenseman Ben Hutton and Derek Forbort plus forward Trevor Lewis. … Rangers defenseman Brady Skjei played his 300th career game. … The Kings won the previous meeting 3-1 on Dec. 10 in Los Angeles. … The Rangers played their 30th home game. They have 17 road games remaining.
Rangers: Visit Winnipeg Jets to start a three-game road trip on Tuesday.
Kings: Host Calgary Flames on Wednesday at Staples Center.