Jeter also doubled in the game, scored two runs and became the first player to reach 3,000 hits in a Yankees uniform.
Boggs, Rickey Henderson, Dave Winfield and Paul Waner are all members of the club and each played for the Yankees, but all four reached the illustrious plateau with different teams.
As he circled the bases with just his third home run of the season and first at Yankee Stadium in nearly a year, Jeter's teammates leaped out of the dugout and met him at home plate for a brief celebration. Longtime teammate Jorge Posada was the first to greet him, followed by Mariano Rivera. He then acknowledged the cheering crowd after reaching the dugout.
The 37-year-old veteran became the fourth-youngest member of the club, as only Ty Cobb, Hank Aaron and Robin Yount accomplished the feat at an earlier age. He also became the first player to record hit No. 3,000 at historic Yankee Stadium, past or present.
Another tidbit: Jeter was only the second player to record five hits in the game in which he reached 3,000. Houston's Craig Biggio did it in 2007 and was the last player to reach the 3k milestone before Jeter.
Boggs, who played with Jeter when he was a rookie in 1996, said in a statement that he had no doubt the Yankee shortstop would one day reach the milestone.
"He is a very consistent player and he never deviated from his game," said Boggs. "When you stay healthy and you are consistent and compile a lengthy career like Derek has done, you have the opportunity to reach that 3,000-hit plateau."
Other members of the 3,000-hit club issued statements Saturday congratulating Jeter, including Paul Molitor and Yount.
"To have the most hits for the most prestigious franchise in all of sports is pretty special," said Molitor, who ranks eighth on the all-time list with 3,319 hits.
Yount, who is 16th on the list with 3,142 hits, said he didn't realize how special the milestone was until his career was ending.
"I love what I see of Derek Jeter. He is the complete package: a leader, clutch player, and lots of success on baseball's biggest stage, New York," Yount said. "Being the complete package is something every player dreams of."
New York City mayor Michael Bloomberg said in a statement that Jeter was a city icon long before he got his 3,000th hit "because he represents what is best in the spirit of our city: an unbreakable belief that with hard work and determination, anything can be accomplished."
"Perhaps above all else," Bloomberg said, "Derek is someone who loves this city and who has a long history of giving back to the place and the people that helped make him the superstar he is. New York has a greater baseball tradition than any other city, but we've never had a player get all 3,000 hits in a New York uniform until today."
After Friday's game was rained out, delaying the inevitable, Jeter's first hit of the day came during a lengthy at-bat. He battled Price into a full count, taking a pair of close pitches that could have been called third strikes, then fouled off a couple more before bouncing a single through the left side of the infield for hit No. 2,999.
The Yankee captain was six hits shy of the mark when a strained right calf sidelined him in mid-June. He returned to the lineup on July 4 after missing three weeks and went 0-for-4 against Cleveland before stroking three hits over the next two games. After a double in the first inning of Thursday's contest against Tampa Bay, he went hitless in his next four trips to the plate.
Jeter, in his 17th major league season, was selected by the Yankees with the sixth overall pick of the 1992 draft and reached the majors in 1995. The first hit of his career was a seeing-eye single through the left side of the infield on May 30, 1995 against Seattle's Tim Belcher.
Two years ago, Jeter passed Lou Gehrig's franchise hit mark of 2,721 and Luis Aparicio's record for hits (2,673) by a shortstop.
Jeter's five World Series rings are the second-most among members in the 3,000-hit club. Only Eddie Collins, who won six, has more.