Jones now has 1,042 extra-base hits and trails only Hall of Famer Eddie Murray, who had 1,099 in his 21-year career.
Jones said it meant a lot to pass Rose, especially since Rose has 1,570 more hits than him.
"Pete had a lot of doubles, a lot of doubles," Jones said. "It's another one of those cool milestones when you sit back from the ballgame and just say, 'Wow.'"
Jones has already become the all-time leader in career RBIs by a third baseman this season, passing George Brett.
Jones has 24 extra-base hits this season, including 10 home runs. Sunday's home run moved Jones past Angels first baseman Albert Pujols into 32nd on the career home run list with 464. Jones is one behind Hall of Famer Dave Winfield.
Teddy Cahill is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.