His catch completed a three-score fourth quarter that saw the Giants (3-1) come back from a late 10-point deficit.
Nicks ended with 10 catches for 162 yards and Victor Cruz added six grabs for 98 yards for New York.
Eli Manning went 27-for-40 in the passing department for 321 yards and two touchdowns as the Giants took their third straight win.
Arizona (1-3) was led by Beanie Wells, who scored three times on 27 carries for 138 yards.
Celebrity Families of 2014 [PHOTOS]