But a reshuffle at the break saw Rafi Leeker's brace and Rob Jacobs' 87th minute strike complete the cup win.
Flixton joint-manager Stuart Delmonte said: "We have to go behind before we wake up, it seems.
"It is not a good habit to get into, but I could not fault my players for showing the desire to come back and win.
"We were playing a team from a higher division, so it was always going to be an uphill task.
"But we changed the formation at half-time and everyone responded."
Report by Darren Witcoop