The hosts laid the foundations for a convincing victory by engineering a none-too-flattering 1-8 to 0-4 interval lead.
Two points apiece by the lively pair of Caoimhín O’Reilly and Niall Clerkin fired the hosts into a 0-6 to 0-1 lead after 14 minutes.
Eamon Wallace’s fourth-minute point had Meath level but they were to play a poor second fiddle for the remainder of the first half.
Cavan’s greater bite in the tackle and greater pep in their step at the business end of the field had Meath pushing the frustration buttons and Bryan McMahon and Pádraig McKeever were fortunate to get away with just yellow cards.
After Bryan Menton’s swirling effort made it four wides for the visitors, team-mate Graham Reilly had better luck to cut Cavan’s lead to a slightly more manageable 0-7 to 0-2 in the 25th minute.
Moments later, Cavan extended their advantage when Conor Moynagh reacted quickest to rifle the ball to the net after Adrian Cole’s shot rebounded off the upright.
Just to rub further salt into Meath’s wound, Cavan brought on their heavy artillery from the bench at half-time with Gearoid McKiernan and Cian Mackey joining the fray.
And just nine minutes after the restart, Cavan had their second goal with Ciaran Brady’s effort firing them into a 2-10 to 0-6 lead and the game looked over as a contest.
Despite landing four balls into the arms of Cavan ‘keeper Galligan, Meath hung in there though and a 49th minute converted penalty by Donal Lenihan gave them hope.
“A brilliant diving save by Meath netminder Colgan denied McKiernan a goal in the 54th minute as the Ulster men sought to see the game out.
The winners-elect lost control of the final quarter for long periods but Meath couldn’t produce the goals they so badly needed to rescue this tie.
Cavan 2-14 Meath 1-12
R Galligan (0-1,’45); N Murray, P Faulkner, D Phillips; M Reilly, C Brady (1-0), E Flanagan; K Clarke (0-1), B Magee (0-2, 2f); D McVeety (0-1), C Moynagh (1-0), O Kiernan; C O’Reilly (0-3, 1f), A Cole (0-1), N Clerkin (0-3).
G McKiernan (0-2) for A Cole (h-t); C Mackey for N Clerkin (h-t); J McLoughlin for D Phillips (51); S Murray for E Flanagan (54); T Galligan for C O’Reilly (63); R Connolly for B Magee (68).
A Colgan; S Lavin, C McGill, D Keogan; B Conlon, B Power, S McEntee; B Menton (0-2), A Flanagan; J McEntee, P McKeever (0-3, 2f), G Reilly (0-2); E Wallace (0-2), C O’Sullivan (0-2), B McMahon.
D Lenihan (1-0, pen) for B McMahon (h-t); H Rooney for A Flanagan (42); S Tobin for J McEntee (55); D O’Neill (0-1) for B Conlon (55); C Halligan for H Rooney (B.C, 60); T O’Reilly for G Reilly (62).
C Brannigan (Down)