Jones had a first-inning double that scored a run, and his fifth home run of the season capped a three-run fifth inning to account for the bulk of the Baltimore offense.
Jason Hammel (2-0) got the win with a 10-strikeout performance over six innings. He allowed six hits and two runs.
Orioles closer Jim Johnson got the first two outs in the ninth but walked A.J. Pierzynski, allowed a single to Adam Dunn and hit Paul Konerko with a pitch to load the bases. However, he retired Alex Rios on a called third strike to end the game and collect his sixth save.
The RBI double by Jones was followed by a run-scoring grounder by Nick Johnson. Chicago tied the score in the third with RBI from Dunn, who doubled, and Konerko, who singled.
Konerko walked, took third on a Rios double and scored on an out in the eighth for the other White Sox run.