Chido Obi put the young Reds ahead after 14 minutes and, after Luke Towler levelled things up for the visitors, Daniel Armer headed home to give United the lead at the break.
Travis Binnion's men extended that advantage after the interval through Ethan Ennis and looked set for victory before Errol Mundle-Smith pulled it back to 3-2 with 20 minutes left to play.
United kept calm though and restored our two-goal gap as the contest entered its final 10 minutes through substitute Jack Fletcher, ensuring a second victory in five days after Monday's win at Middlesbrough in our competition opener.