United were value for the win, even though it was a very poor end-of-season match, but it ensures they will finish above Sunderland in fifth position in Reserves League North.
Newcastle coach Tommy Craig sent on Academy striker Andy Carroll at half time and within 45 seconds of the restart he created United's winning goal.
Craig Baxter launched a throw-in from the right touchline, Carroll at the near post headed on, and Finnigan moved in unmarked to place a five-yard header into the right corner.
NEWCASTLE UTD RESERVES: Forster, Baxter, Farman, Atkin, Edgar, Gate, Huntington, Cavener, Finnigan, Troisi (Carroll, 45), A O'Brien.
Subs not used: Cave, Shanks, Cook.
Attendance: 502.