Beckham completed a 40-yard pass on a trick play.
The Los Angeles Rams are on the verge of a 34-11 win over the Arizona Cardinals after a play-off touchdown by Beckham Jr.
The three-time Pro Bowler made four catches for 54 yards as the Rams dominated the first half.
Beckham made a 40-yard pass on a trick play to set up the Rams' fourth touchdown.
LA will play the Tampa Bay Buccaneers next week.
The last team to lose their perfect record was Arizona, who lost four of their last five games.
They were never in it at LA's Sofi Stadium, which will host Super Bowl 56 on 13 February, despite having an 8-1 record on the road.
Beckham made an acrobatic catch at the back of the end zone in the first quarter to give the Giants a 17 yard touchdown.
Beckham had six touchdown catches in nine games for the Rams, who added him to their star- studded squad after the Cleveland Browns decided to release the receiver.
Matthew Stafford scored on a quarterback sneak for his first rushing touchdown since 2016 and David Long Jr scored on an pick six after Kyler Murray threw the ball away from his own end zone.
The third-year quarterback couldn't get the offence going in the first half and Beckham showed him how it's done in the third quarter, making a huge play across the field to Cam Akers.
Stafford found Cooper Kupp for a seven-yard touchdown on the second play of the second quarter.
The final team to progress from the first round of the play-offs was the Rams.
It was the first post-season win for Stafford in 186 games in the league, since he was traded to the Rams from the Detroit Lions.
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Kick-offs in the morning and away teams first.
Saturday, 22 January.
The Cincinnati and Tennessee teams are playing a football game.
The 49ers are playing the Packers.
Sunday, 23 January.
The LA Rams are playing the Tampa Bay Buccaneers.
The Buffalo Bills are playing the Kansas City Chiefs.
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