This is only the second triumph for the "blues" in the last nine matches, and the previous one was achieved in this competition against lower league team Port Vale.
Thus, interim manager Callum McFarlane made his debut with a victory, after succeeding Liam Rosenior on the bench until the end of the season a few days ago.
The decisive goal was scored by Enco Fernandez on a cross from Pedro Neto in the 23rd minute.
The FA Cup final is scheduled for May 16th at Wembley.