Rodriguez, a three-time AL MVP, homered on the first pitch he saw from Detroit's Justin Verlander, hitting a 95 mph fastball into the seats in right field in the first inning Friday night, a game New York won, 7-2.
Rodriguez became the 29th player in Major League Baseball history to reach the mark and took a brief curtain call. It was the fourth game in a row he homered off Verlander.
On July 9, 2011, Jeter became the 28th member of the 3,000-hit club with a home run in the third inning against Tampa Bay's David Price, who currently pitches for the Tigers.
Adam Warren (5-4) did his part to hold down the Tigers. The right-hander threw a career-high eight innings, allowed seven hits and two runs. He had seven strikeouts without a walk, as the Yankees posted their third consecutive win.
Brett Gardner went 4-for-5 with three RBI and snapped a tie with a two-run homer in the fifth inning. Didi Gregorius also went deep off Verlander, who was making his 300th career start and only second of the season since recovering from a right triceps strain.
Verlander (0-1), who fell to 0-4 in eight starts at Yankee Stadium, allowed 10 hits and six runs over 6 2/3 innings.
Bryan Holaday hit a two-run single in the second inning for the Tigers, who lost their third straight game.
Gregorius homered to right in the home second and Gardner belted his seventh long ball of the year, a blast to right-center with Mason Williams aboard to provide a 4-2 New York lead.
Warren retired 11 straight batters until Ian Kinsler led off the sixth with a single. Kinsler went to third on Miguel Cabrera's base hit to right, and tried for home when the throw got away from third baseman Nick Castellanos. The throw home was in time as John Ryan Murphy applied the tag to Kinsler's leg.
The Yankees expanded their lead in the seventh inning thanks to the speedy Gardner, who bunted for a hit with one out and went to third on Chase Headley's single. Verlander then uncorked a wild pitch. Holaday tracked down the ball, but the catcher's scoop to Verlander covering was a tad late as Gardner slid head-first into home.
New York tacked on another run in the eighth when Gardner singled to left to drive in Chris Young, who doubled.
The Detroit Tigers reinstated slugger Victor Martinez from the 15-day disabled list. Martinez, who was out due to inflammation in his surgically repaired left knee, singled and scored on Holaday's hit. The Tigers opened a roster spot for Martinez by optioning outfielder Tyler Collins to Triple-A Toledo on Thursday ... The Yankees placed pitcher Sergio Santos on the 15-day disabled list and recalled pitchers Bryan Mitchell and Branden Pinder from Triple-A Scranton/Wilkes-Barre. The Yankees also optioned pitcher Chris Martin to Scranton/Wilkes-Barre ... Cabrera went 2-for-4, but had his six-game streak with at least one RBI snapped ... Warren is 3-0 in six meetings against the Tigers ... Rodriguez finished 1-for-4.