Earlier in the day, Rodriguez' retirement announcement came 21 years after the fan favorite known as Pudge made his major league debut as a 19-year-old with the Rangers and later played for five other teams.
"It's a very hard day for me," Rodriguez said. "It's been a great, great run . . . It's been beautiful."
Rodriguez plans to remain in baseball in some capacity, and Rangers president Nolan Ryan said there already have been some preliminary discussions about making that happen.
He caught a major league record 2,427 games, surpassing Carlton Fisk's record of 2,226 during a game for the Houston Astros 3 years ago at Rangers Ballpark. It was later that season that Pudge returned briefly to the Rangers, the team he played for the first 12 of his 21 seasons.
Rodriguez hit .296 with 311 home runs and 1,332 RBI in 2,543 games overall with Texas (1991-2002, 2009), Florida (2003), Detroit (2004-08), the Yankees (2008), Houston (2009) and Washington (2010-11). His 13 Gold Gloves were the most for a catcher.
CC Sabathia (2-0) struck out eight over eight innings.
The big lefthander was pitching with an extra day of rest after the Yankees' scheduled series finale at Boston was rained out Sunday night, a day after New York overcame a 9-0 deficit for a 15-9 win over the Red Sox.
Mariano Rivera worked a perfect ninth for his fourth save.
Third baseman Adrian Beltre was out of the Rangers' lineup for the third straight game with a sore left leg.
In other games *
At Kansas City, Jose Bautista hit a two-run homer, Kelly Johnson also went deep and the Toronto Blue Jays beat the Royals, 4-1, to complete a four-game sweep. Kansas City lost its 11th straight to finish up a winless 10-game homestand.
* At Oakland, Jake Peavy (3-0) threw a two-hitter as the Chicago White Sox blanked the Athletics, 4-0.
* At Minneapolis, Cody Ross homered twice, tying the game with a two-run shot in the seventh inning and giving Boston the lead with two outs in the ninth as the Red Sox beat the Twins, 6-5.