Rodriguez, now with the Houston Astros, caught his 2,226th career game against Texas, the team for which he made his major league debut at age 19 on June 20, 1991.
Pudge matched Carlton Fisk, a Hall of Famer who played for Boston (1969-80) and the Chicago White Sox (1981-93).
Rodriguez, a 14-time All-Star who has won 13 Gold Gloves, played his first 12 seasons with Texas before the team refused to offer salary arbitration after the 2002 season. He won a World Series with Florida in 2003, then spent the past five seasons in Detroit before signing a $1.5 million, one-year deal with the Astros during spring training.
When Rodriguez was introduced before the game Tuesday night, and each time he came to bat, he got a warm reception from the Rangers fans. He got a standing ovation when he led off the fifth inning with his sixth homer of the season.
Rodriguez caught 1,426 games in Texas, second on the team list to Jim Sundberg's 1,495 games. Pudge was part of the Rangers' three AL West championship teams in 1996, 1998 and 1999. He was the AL MVP in 1999, when he hit .332 with career highs of 35 home runs and 113 RBIs.
The home run Tuesday night was his 108th in Rangers Ballpark, his third there as an opposing player. Only Rafael Palmeiro (130) and Juan Gonzalez (115) have hit more homers in the stadium.
Fisk's final game was June 22, 1993 in Chicago against Texas, a game in which Rodriguez made his 263rd career appearance behind the plate for the Rangers.
Rodriguez had been tied with Bob Boone, who caught 2,225 games over 19 seasons with Philadelphia (1972-81), the California Angels (1983-88) and Kansas City (1989-90).
Astros manager Cecil Cooper has already said that Rodriguez will catch Wednesday, which would break the tie with Fisk.
The 37-year-old Rodriguez sounds like he plans to keep adding to the mark long after that.
"I've still got years left in the tank," Rodriguez said before Tuesday's game. "I love and enjoy this game."