Antrim cut an eight-point deficit to three at one stage but a late goal by Sean Quigley ensured Pete McGrath's Erne men would progress.
Home forward Tomas Corrigan landed nine points but boss Pete McGrath will be concerned about the second-half wobble.
Fermanagh had led 0-9 to 0-2 at half-time before Antrim hit back with five scores without reply.
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The Erne men now progress to play Donegal in the last eight of the provincial championship.
Antrim left their challenge much too late and ultimately paid for a shockingly slack start.
The Saffrons, who won promotion to Division Three earlier in the year, were six points down when they registered their first score through a Brian Neeson free.
The gap was eight late in the first half and it looked like Fermanagh were going to stroll into the quarter-finals.
But from 0-11 to 0-3 down, Antrim rallied with five unanswered points by Mark Sweeney, John Carron, Tomas McCann, Ryan Murray and Sean Burke.
During that spell, Neeson had a goal chance but shot into the side-netting from a tight angle.
The momentum was with Antrim but they conceded a cheap free to give Corrigan the chance to give the hosts a four-point lead before Quigley netted the only goal.
Top scorer Tomas Corrigan: "The first half was the most pleasing thing. We targeted a big first 10 minutes and wanted to keep going after that.
"That is what we did but we are disappointed with our second half performance. We have a lot to work on."
Fermanagh manager Pete McGrath: "For long periods in the second half we were sleepwalking.
"It was a nervous time for us. We let Antrim back into it and that is a concern.
"The result was satisfactory but the performance overall you have to say we did OK but can do better."
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Antrim joint manager Gearoid Adams: "We did not turn up in the first half. There were 14 scoring chances each which is hard to believe.
"In the second half we got it back to three but Fermanagh kicked on in the end and the goal put a gloss on it for them.
"We came down here to win and we are disappointed that we didn't."
Victorious Fermanagh now face Donegal in the last eight of the Ulster Championship while Antrim go into the All-Ireland qualifiers.
Fermanagh: C Snow; M Jones, C Cullen, M O'Brien; D McCusker (sub D Kelly 66), J McMahon, B Mulrone; E Donnelly, A Breen; P McCusker (sub P Cadden), R Jones, R Lyons; R Corrigan (sub D Teague 56), S Quigley, T Corrigan.
Antrim: C Kerr; K O'Boyle, R Johnston, N Delargy; P McBride, M Johnston, J Laverty (sub McAleese 47); M Sweeney, C Murray (sub S McVeigh HT); M Fitzpatrick (sub R Murray 56), K Niblock, J Carron; B Neeson (sub S Burke 59), T McCann, M McCann.
Attendance: 9124
Fermanagh saw off a mini-revival from Antrim to book an Ulster Championship quarter-final meeting with Donegal.