The White Sox went on to win 15-5.
"Four hundred is great. It's a good milestone to get," Jones said. "A lot of people don't get there. But I'm just happy to get it over with and look forward to just going out there and having success and helping this team get to the playoffs."
Jones became just the second player in a White Sox uniform to hit his 400th home run, joining Frank Thomas. He also moved into sole possession of 46th on the all-time home run list, breaking a tie with Andres Galarraga and Al Kaline.
Jones already has 12 home runs this season, after hitting 17 a year ago with the Texas Rangers. He hit just three in 2008 as a member of the Los Angeles Dodgers after spending the previous 12 seasons with the Atlanta Braves.
Jones' three-run shot was one of four home runs in a seven-run third inning for the White Sox. The four home runs tied a team record for most in an inning, the sixth time it has happened and first since Aug. 14, 2008, when they hit the four in succession against the Royals.