Wood (2-1) allowed three hits while striking out six and Kevin Gregg secured the victory with his third save as the Cubs notched a third straight win over the reeling Marlins.
DeJesus went 2-for-4 and drove in the decisive run with a seventh-inning single. Luis Valbuena added two hits and an RBI for Chicago.
Marlins starter Alex Sanabia (2-3) surrendered three runs on six hits and two walks over 6 2/3 frames.
Giancarlo Stanton and Miguel Olivo each belted a solo homer in Miami's eighth loss in 10 games.