Olt, a 2010 first-round draft pick, took Mariners starter Randy Wolf deep in the second inning for his first home run of the night.
Baez gave the Cubs a 2-1 lead with a homer off Wolf in the top of the fourth.
Olt started a four-run sixth inning with his second home run. Catcher John Baker finished 2 for 3 with a three-run double in the sixth.
Baker cleared the bases after three Mariners' errors in the inning.
Seattle shortstop Brad Miller helped his cause as he battles another young player, Nick Franklin, for the starting job. Miller homered, singled and drove in two.
Mariners catcher John Buck drove in the tying runs with a two-out single in the bottom of the ninth.
Abraham Almonte scored the winning run on a Ty Kelly single in the 10th.
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