Boro, who sit seven points clear at the top of the Northern Premier League having won 12 of their opening 13 matches, transferred that form into their latest cup outing at Broadhurst Park.
Jamie Morgan marked his return to the starting line-up with a quickfire first-half double to give Radcliffe a healthy lead at the break.
However, they were pegged back eight minutes after half-time by FC United, before Michael Donohue struck three minutes from time to take the game to penalties.
Goalkeeper Mateusz Hewelt proved to be their hero, making a decisive save from Charlie Oliver's spot-kick as his team-mates enjoyed a perfect five from five from 12 yards out to advance to the next round of the competition.
"I thought we were fantastic in the first half, as good as we've been," he said.
"We handled the ball really well. The pitch was tough, I'd go as far as saying it's the smallest pitch we've ever played on at this level of football, in terms of compactness and narrowness.
"I thought it might take us a bit more time to get used to, but it didn't. We started really well and it could've been three or four-nil at half-time.
"In the second half we looked leggy. If you think about the last week, we've played three games - two of them away and one with 10 men against a good side. It caught up with us a little bit.
"We're down to the bare bones at this moment in time. It's not a moan - we're still playing well and the lads are doing what we've asked.
"I must caveat that by saying FC United really upped the tempo in the last 30 minutes and were banging our door down without really creating anything.
"We dropped a bit deeper and they were on a front foot, they played it as a cup game and committed bodies forward.
"You've always got a chance with Matt in goal and the quality of players that we've got taking penalties."
The reward for Radcliffe's penalty shootout triumph is a trip to National League North side Farsley Celtic in the next round of the competition.
Boro are one of eight NPL teams at Step 3/4 level to remain in the FA Trophy.
Second round ties will take place on Saturday 18th November, with winners receiving £3,750 and losers £1,000.
Games involving NPL teams:
Buxton v City of Liverpool
Alfreton Town v Macclesfield
Curzon Ashton v Matlock Town
Farsley Celtic v Radcliffe
Nantwich Town v Chester
Stafford Rangers v Brackley Town
Harborough Town v Chelmsford City
Hemel Hempstead Town v Walsall Wood
Photo credit: Darren Murphy