Alvarez (3-3) yielded three runs on seven hits until coming out the game in the seventh with a tight hamstring. The right-hander walked one and struck out three.
After allowing the Cubs to grab a 3-1 lead in the first inning, Alvarez himself wrested back the lead in the second.
Mike Dunn and Chad Qualls teamed up for two innings of shutout relief and Steve Cishek notched his 29th save as Miami claimed the opener of a three-game set.
Wood (8-11) surrendered four runs on nine hits over seven innings.
Dioner Navarro went 2-for-4 with an RBI for Chicago.
Celebrity Families of 2014 [PHOTOS]