Rodriguez' solo shot on the first pitch of the fifth inning put him past Ken Griffey Jr. and 29 homers behind Willie Mays' fourth-place total of 660. Nick Swisher and Russell Martin also connected for New York, and Derek Jeter moved into 18th place with his 3,111th career hit, passing Dave Winfield.
The victory came exactly 100 years after the Red Sox beat the Yankees' forerunner, the New York Highlanders, 7-6 in 11 innings, and one day after Curtis Granderson hit three of New York's four homers in a 7-6 win over the Minnesota Twins.
Clay Buchholz (1-1) allowed all five homers in losing for the first time in 12 starts. Josh Beckett also served up five homers in the Red Sox second game of the year, a 10-0 loss at Detroit.
Ivan Nova (3-0) won his 15th consecutive regular-season start, allowing two runs on seven hits with no walks and five strikeouts in six innings.
Both teams wore throwback uniforms similar to those used in Fenway's first major-league game. The Red Sox had off-white uniforms and caps with the only printing on either being the words "Red Sox" in red across the chest. The Yankees uniforms were all grey with the only printing the letters "NY" on the caps and left breast. It is believed to be the first time the Yankees have worn throwbacks.
The Red Sox lost their fourth straight game, a span in which they've been outscored 31-8.
Some outstanding players took the field for the Red Sox. Unfortunately, most of them were among the about 200 retirees who strolled to their positions during pre-game ceremonies marking the anniversary. They included Hall-of-Famers Carl Yastrzemski, Carlton Fisk, Jim Rice, Bobby Doerr and Dennis Eckersley plus Pedro Martinez, Luis Tiant, Nomar Garciaparra, Mo Vaughn and Johnny Pesky.
Terry Francona, let go as manager after last year's September collapse that cost the Red Sox a playoff berth, received one of the loudest ovations. New manager Bobby Valentine has been booed several times by the home crowd as the Red Sox (4-9) have gotten off to another slow start after opening last season at 2-10.
Buchholz's beginnings haven't been good either. He allowed four runs in each first inning of his other two starts. On Friday, he gave up only one run in the opening inning. But by the time he left after walking Granderson to lead off the seventh, he had allowed six runs on nine hits and two walks with just two strikeouts.
The Yankees led 1-0 three batters into the game. Jeter reached on an error by second baseman Dustin Pedroia, who lost his popup in the sun. He moved up on a wild pitch and scored on Rodriguez's single.
They needed only three batters again to take a 3-0 lead in the second. Swisher led off with a homer, Raul Ibanez grounded out and Chavez drove an 0-2 pitch into Boston's bullpen in right-center field.
David Ortiz cut it to 3-1 leading off the second with his second homer of the season. Umpires originally ruled that the ball had not gone out but, with Ortiz standing on second, they viewed a replay of the hit and reversed the call.
The Yankees stretched their lead to 5-1 on leadoff homers by Chavez in the fourth and Rodriguez in the fifth. They were the second homers of the year for both.
The Red Sox made it 5-2 in the bottom of the fifth when Cody Ross doubled and Mike Aviles was credited with a double when right fielder Swisher lost his fly ball in the sun. Martin homered in the sixth.
Notes: Freddy Garcia (0-1) pitches for the Yankees against Felix Doubront (0-0) on Saturday's second game of the three-game series. ... The Yankees had nine homers in their previous four games, all against the Twins. ... Boston's Ryan Sweeney hit safely for the 10th time in his 11 games. ... Nova won for the first time in four starts against the Red Sox. He began the game 0-2 with a 6.62 ERA in those games. ... Friday was the 73rd anniversary of Ted Williams' major-league debut.
Associated Press
