Striker Aaron O'Connor hit the York post after rounding keeper Michael Ingham and seconds later Jamie Stuart's header was scrambled off the line.
But Brodie's near-post strike from a corner sealed York's ninth win from 10.
Rushden & D'monds: Roberts, Osano, Downer (Ainsley 46), Stuart, Robinson, Byrne, Porter, Terry (Akurang 81), Tomlin, Louis (Farrell 73), O'Connor. Subs Not Used: Day, Pattison.
Ingham, Parslow, Graham, McGurk, Meredith, Lawless (Ferrell 90), Mackin (Smith 61), Barrett, Carruthers, Rankine (Gash 62), Brodie. Subs Not Used: Mimms, Gall.
Goals: Brodie 73.
Ref: David Coote (Newark).