Marson's two-run double in the second put the Indians ahead 3-0 and Valbuena's solo shot in the sixth gave the Tribe a 4-2 advantage.
Ubaldo Jimenez (3-2) overcame five walks in six innings to collect the win, yielding two runs on three hits while fanning two.
Chisox starter Zach Stewart (2-4) was touched for three runs on seven hits before exiting after five frames.
Juan Pierre and Alexi Ramirez each went 2-for-5 with an RBI for Chicago.
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