United were missing Ryan McBride, Jason Taylor and Scott Dartnall, which as a result saw Sean Ray leading the line and Ray came close to opening the scoring after an early header rebounded off the crossbar.
United opened the scoring with just under 30 minutes played as a foraging run by Matt MacLean ended in a handball inside the area and a penalty awarded.
Wes Tate stepped up and placed his penalty into the roof of the net.
Further chances fell to Ray, Tate and MacLean in the second half but United were reduced to 10 men midway through the second half after Jack Franklin was dismissed for a reckless tackle.
Oakwood applied pressure onto United after the red card, but were unable to trouble Grant Young.
In time added on, Ray made the victory secure as he converted a through ball for his second goal in as many matches.
United return to action on Saturday afternoon when they travel to take on Combined Counties Premier League leaders South Park in Round Three of the FA Vase