The Royals had grabbed a 7-6 lead in the top of the seventh inning on Alcides Escobar's two-run single, but St. Louis stormed back with three of its own.
The Cards put two on with one out against Tim Collins (4-1), then Holliday (4-for-5, solo homer) delivered a score-tying base hit off Greg Holland.
Allen Craig coaxed a walk and one out later Molina supplied a two-run single, icing the victory and evening the three-game series at Busch Stadium.
Molina also smacked a two-run homer, finishing with four RBI, while Mitchell Boggs (1-1) earned the Cardinals' third win in four games with 1 1/3 scoreless frames.
Mike Moustakas went 3-for-5 with four RBI, including a solo homer, while Alex Gordon added three hits in the Royals' loss.