Hamilton's towering 412-foot solo shot into the second deck of right-field seats came in the first off Tim Hudson (7-5), who is winless his past five starts.
Mark Teixeira, sent from Texas to Atlanta in a trade deadline deal last July, was 0-for-2 with a sacrifice fly and a walk in his first game against the team which drafted him fifth overall in 2001. Teixeira made his major league debut with the Rangers in 2003.
Bradley, the AL batting leader at .330, had a two-run single in a four-run outburst in the third. He sustained a mild left quadriceps strain running the bases after hitting the ball into the right-center field gap. Bradley reached down before even getting to first base, then pulled up without making the turn.
After manager Ron Washing-ton and a trainer went to check on him, Bradley ran a sprint down the right-field line. He then went to the dugout and was replaced by Brandon Boggs. The Rangers said Bradley would be re-evaluated today.
It was only the fourth game since interleague play began in 1997 matching the leading hitters from each league. NL leader Chipper Jones was the DH for Atlanta, going 0-for-2 with two walks, dropping his average three points to .400.
Vicente Padilla (9-3) allowed two hits over six innings with four strikeouts for Texas.
C.J. Wilson worked the ninth for his 14th save in 16 chances.
Texas built a 6-0 lead before Omar Infante led off the Atlanta sixth with his first homer since last July. No. 9 hitter Gregor Blanco then walked, went to third when Hamilton dropped a flyball in right field and scored on Teixeira's sac fly to center.
Marlon Byrd's homer in the bottom of the inning put the Rangers up 7-2.
Hudson, 0-2 since his last victory May 22, threw 17 of his 21 pitches for strikes in the first two innings. One of those was the homer by Hamilton, but he then got three outs in the second on only nine pitches.
But Gerald Laird hit the first pitch of the third for a single, and Ramon Vazquez followed with another single on a 1-0 pitch before Ian Kinsler walked.
Michael Young hit what appeared to be a double-play grounder to second base, but Kinsler made a strong slide to prevent shortstop Yunel Escobar from making a good relay throw while Laird scored. Hamilton drew a walk to reload the bases before Bradley's big hit.