Viciedo finished with five RBI and Adam Dunn went 2-for-4 with a pair run-scoring singles for the White Sox, who pounded out 15 hits to take the opener of a season-ending three-game series.
Hector Santiago (4-1) gave up only one hit over seven stellar innings, during which he struck out 10 and issued a single walk. The rookie left-hander threw 78 of his 108 pitches for strikes in his fourth major-league start.
The second-place White Sox came into the contest needing three wins and three losses by the American League Central-leading Detroit Tigers to keep their playoff hopes alive.
But the Tigers bested Kansas City Monday to clinch the division.
Indians starter Corey Kluber (2-5) surrendered four runs on five hits in a 5 2/3-inning appearance.