Nix launched solo shots in the second and eighth innings and Shin-Soo Choo went 3-for-3 with a pair of runs driven in to pace the Indians, who evened their four-game series with the Royals at a win apiece.
Asdrubal Cabrera added three hits and an RBI to back Tomlin (5-4), who registered a four-hitter, allowing three runs, walking two and fanning six in a 112-pitch effort.
Luke Hochevar (6-6) was tagged for four runs on eight hits in a five-inning start for the Royals.
Wilson Betemit drove in all three Kansas City runs with a two-run homer and a sacrifice fly.
Notable deaths of 2014 [PHOTOS]