Rivera lined a ball from former teammate Scott Kamieniecki into the right-center field gap Sunday and kept running when he saw center fielder Jeff Nelson slowly pursuing the ball.
The five-time World Series champion scored standing up when the relay throw hit a YES Network cameraman positioned behind the mound.
"All those years, those 19 seasons that I played, I always knew when Old-Timers' Day was going to be," Rivera said. "I was here early for all those games. ... Now for the first time, to be called an Old Timer, it's amazing. I had a great time today."
Rivera retired after the 2013 season with a Major League-record 652 saves. He was named the National Baseball Hall of Fame's first unanimous inductee in January.
Rivera was hitless in three at-bats during his Major League career from 1995 to 2013. He walked with the bases loaded in a June 2009 victory over the rival Mets for his first career RBI.
Rivera also returned to the mound with his trademark entrance song, Metallica's "Enter Sandman," playing from the loudspeakers. The longtime closer even saw action in center field.
"[It was] a good time seeing the guys, being on the field ... it's amazing," Rivera said. "That's what I love, that's what I always did. I thank God for a beautiful day, seeing the guys for the first time in years. It was outstanding."