The Royals need to take full points from their trip to Ennis next week and hope already promoted Kildare can do them a favour against Galway.
Sean Quigley (free) and Ryan Lyons had early points for Fermanagh but that was as good as it got for Pete McGrath’s side.
From the time Donal Lenihan netted from the penalty spot on 14 minutes, the hosts were in control.
They led 2-6 to 0-4 at the break with the second goal a fine individual effort from Bryan McMahon on 22 minutes.
Meath boss Andy McEntee said the performance was a strong reaction from the display in Páirc Uí Rinn a week earlier.
“From the very start you couldn’t question their workrate,” said McEntee.
“We got a lot of tackles in, a lot of turnovers in, in the first half, against the wind and I suppose when you go in eight points up having played against a strong wind it really sets you up for the game.”
“We weren’t happy with certain things last week and we picked what we thought was the best team to do a job today...
There was enough made of what was said after the game last week so they obviously took it on board. That’s the good thing about this league, you get a chance pretty much straight away to put things back on the right track.”
Wing forward Alan Forde limped out of the action after 10 minutes — McEntee said it was possibly a cruciate.
Meath added a further 1-3 before midfielder Lee Cullen hit Fermanagh’s first point of the second half. That third Meath goal was fisted to the net by Sean Tobin following a high delivery from Graham Reilly.
B McMahon (1-3), S Tobin (1-2), D Lenihan (1-1, 1-0 pen), C O’Sullivan (0-3), G Reilly, J McEntee (0-2 each), J Toher (f), B Menton (0-1 each).
S Quigley (0-2, frees), K Connor, L Cullen, E Courtney (free), R Lyons (0-1 each).
P O’Rourke; D Keogan, C McGill, D Tobin; S McEntee, B Power, P Harnan; B Menton, J Toher; A Forde, G Reilly, E Wallace; B McMahon, S Tobin, D Lenihan.
M Burke for Harnan (BC 10), C O’Sullivan for Forde (10), J McEntee for Reilly (51), C O’Brien for Toher (54), A Douglas for Power (62), J Wallace for E Wallace (64).
C Snow; M Jones, C Cullen, K Connor; C P Murphy, B Mulrone, A Breen; E Donnelly, L Cullen; P McCusker, R Jones, R Lyons; E Courtney, S Quigley, J McMahon.
T Daly for M Jones (BC 30), D McCusker for Lyons (46), P Rehill for Murphy (55), C Corrigan for P McCusker (55), D Teague for Courtney (65).
D O’Mahoney (Tipperary)