Called on to hit for reliever Carlos Villanueva, Wood hit a sharp groundball off Jacob Turner down the left field line, scoring Junior Lake for the go-ahead run.
Wood, who is batting .250 this season, was 0 for 4 as a pinch hitter entering the game.
Miami’s Tom Koehler was near perfect to start, retiring 14 of the first 15 batters. Only Mike Olt registered a hit against the Marlins’ starter during that stretch.
But the Cubs overcame a 3-0 deficit in the sixth inning.