Rodriguez hit a three-run homer, his third this season and No. 632 in his career, in the fifth for a 6-1 lead. The Rangers hadn't given up more than five runs in a game before that, and Jeter added an RBI double in the sixth.
''That's a big three-run homer because it kind of breaks the game open a little bit,'' Girardi said. ''And we got a big two-out hit from Curtis (Granderson) in the first.''
New York went ahead to stay when Granderson blooped a two-run single into short right-center in the first. Jeter led off the game with an infield single and Robinson Cano also had a single.
It was the 42nd career four-hit game for Jeter, who is batting .450 (27 for 60) during his hitting streak and raised his season average to .411.
All of his hits came in the first six innings against Holland before he struck out in the ninth against Koji Uehara.
Since returning from the disabled July 4, just days before getting career hit No. 3,000 in a five-hit game, Jeter is hitting .346 over his past 85 games.
''When he went through his struggles last year, there was one thing I wasn't going to do: I wasn't going to doubt him,'' Girardi said. ''I know his heart, I know his character and how hard he works at what he does.''
No. 9 batter Chris Stewart drew a leadoff walk in the Yankees fifth and scored on Nick Swisher's sacrifice fly. Rodriguez homered later in that inning, the ball landing in the reconfigured visitors' bullpen just beyond the left-center wall.
Hamilton's AL-leading eighth homer was a 422-foot solo shot to right-center in the sixth to get Texas within 7-2. The homer came a couple of pitches after his bat flew out of his hands on a swing and landed in the front row of seats past the Rangers dugout.
Before that homer, Hamilton was 1 for 15 with six strikeouts in his career against Sabathia.
No Rangers player had ever reached eight homers quicker in a season -- Hamilton's came in the 17th game. Rodriguez needed 18 games to hit his eighth homer in 2002, his second of three seasons in Texas, when he went on to hit a career-best 57 homers.
Ian Kinsler led off the Rangers first with a single and scored when Hamilton grounded into a double play.