Rios connected for a two-run blast off former White Sox pitcher Jon Garland (1-4) to begin the uprising, while Paul Konerko and Alexi Ramirez each added two-run singles as the Chisox evened their three-game set with the Dodgers at one win apiece.
Konerko went 3-for-5 with three RBI and Brent Lillibridge added a two-run clout in Chicago's lop-sided victory.
Mark Buehrle (4-3) earned the win, limiting Los Angeles to two runs on seven hits over seven innings, walking none and striking out one.
Garland was roughed up for seven runs on 11 hits before getting the hook after 3 2/3 innings.
Jerry Sands hit a solo homer for the Dodgers.