After a day after doubling, singling and driving in two runs in his debut, Jones scored twice to help the Tigers complete a three-game sweep.
Jones hit a leadoff double in the ninth against David Robertson (4-3) and advanced to third on Jarrod Saltalamacchia's deep flyball.
Collins came up as a pinch-hitter and was able to lift the ball to left-center. Avisail Garcia made the catch, but his throw bounced before it even reached the mound.
Francisco Rodriguez (2-3) pitched the ninth.
Jose Abreu and Alex Avila homered on consecutive pitches in the fourth for the White Sox.