From left field, Conine threw out J.T. Snow at the plate, with Rodriguez absorbing a hard collision while holding onto the ball for the final out.
The Marlins defeated the Giants, 7-6, that day at Sun Life Stadium, the club's former home.
"The way we finished that game gave us a little push, to say, 'Wow, we believe this,'" said manager Ozzie Guillen, then the Marlins' third-base coach.
Rodriguez was back in a Marlins uniform on Saturday night, as the team honored the now retired catcher.
Rodriguez took part in a pregame ceremony before the Marlins faced the Nationals at Marlins Park. Wearing his old No. 7 jersey, Rodriguez was presented with a collage of images to recognize his achievements in 2003.
Instead of having Rodriguez throw out the ceremonial first pitch, he took part in a recreating his famous play at the plate.
Conine, now a special assistant with the Marlins, went to left field and made a toss to the plate. In 2003, his throw arrived on one hop, and Rodriguez was able to secure the ball before tagging Snow.
The throw on Saturday was two hops, but it was on target, and Rodriguez fielded it cleanly and simulated a tag.
Trivia buffs will recall Jeffrey Hammonds singled to left off Ugueth Urbina in the ninth. Snow tried to score the tying run from second, but the series ended in dramatic fashion.
"I was surprised about two things," Guillen said of that day in 2003. "They did not pinch-run for J.T. Snow. And I didn't think Conine could throw anybody out from that point. I believe that play was meant to be."
Rodriguez was already a 10-time All-Star when he signed with the Marlins. Winning the World Series in 2003 helped cement the catcher's legacy.
"I got in trouble talking about Pudge two years ago," Guillen said. "I said Roberto Clemente is now No. 3 in Puerto Rico. They say, 'Why?' I say because of [Roberto] Alomar and Pudge. If you look at the numbers and all that stuff, I think Pudge, in my era, is the best catcher I've ever seen.
"To play the way he played and where he played, that's not easy. He played in Texas. To play the way he played, I don't think too many people can handle that. Who's a better catcher than him over the years?"