In the fifth, Rosales had doubled in a run, sandwiched in between solo shots by Yoenis Cespedes in the fourth and sixth, followed by another solo homer by Josh Reddick.
The series-opening win was Oakland's eighth in their last 10. With three more remaining against the struggling White Sox - losers in nine of their last 10 - the A's are hoping to overtake the Rangers by the end of the weekend.
Game two of the series goes off at 8:10 pm EDT in Chicago.
The St. Louis Cardinals are keeping the pedal to the metal, keeping themselves clear of pursuing Cincinnati and Pittsburgh in the NL Central.
The two division leaders knocked out 30 hits (17 by St. Louis) in the slugfest finale of a four game series, split two games apiece.
St. Louis was led by Daniel Descalso, whose two-run homer highlighted the eight-run uprising. Descalso also singled twice and scored once more, going 3-for-4.
Roughed up was Arizona starter, Ian Kennedy, who allowed 10 runs on 13 hits over four innings of questionable mound work.
Despite the loss, the Diamonbacks leave St. Louis 2 1/2 games clear of the Giants and Rockies in the NL West. The Cardinals hold a three-game lead on the Reds and four over the Pirates.
Today's Trivia: Career-wise, who hit more home runs, Ernie Banks or Willie McCovey? (answer tomorrow)
Yesterday's Answer: "Donnie Baseball", Don Mattingly, led the major leagues in doubles three straight years (1984-86) with 44, 48 and 53, respectively.