Stephen Clynch's free-taking proved crucial as Meath recovered from a poor first-half display to come out on top at Pairc Tailteann.
The hosts trailed by 0-4 to 0-8 at half-time but wiped out the deficit within four minutes of the restart before John Meyler put them ahead for the first time on 42 minutes.
They added three more points to that tally, all from frees converted by Clynch, before substitute Fiachra Bradley ended Armagh's second-half scoring drought on 61 minutes.
Clynch eventually took his tally to nine points (eight frees), and with Meyler adding his third point from play, Armagh were unable to close the deficit. The Orchard County enjoyed an abundance of first-half possession, with Declan Coulter accounting for five of those points.
Meyler had Meath's only point from play in the opening period, with their three remaining scores coming from Clynch frees. The sides are also due to play each other in the National League and Christy Ring Cup later in the season.
SCORERS – Meath: S Clynch 0-9 (8f), J Meyler 0-3, A Gannon 0-2, A Watters 0-1. Armagh: D Coulter 0-5 (3f), D Carvill 0-2f, K McKernan, C Carvill, P Breen, F Bradley 0-1 each.
MEATH – S McGann; C Reilly, D Healy, W Mahady; S Brennan, J Toher, A Watters; S Donoghue, J Meyler; E Marsh, S Clynch, P Conneely; A Gannon, M O'Sullivan, P Durnin. Subs: B Slevin for Durnin (24), G Kelly for Marsh (66).
ARMAGH – J Burke; B Breen, C Clifford, C Devlin; J King, N Curry, S Gaffney; J Corvan, K McKernan; M Lennon, D Coulter, P Hughes; P Breen, D Carvill, C Carvill. Subs: F Bradley for Hughes (h-t), B Mallon for Devlin (h-t), C McKee for P Breen (50), N Green for Gaffney (65), T Donnelly for Clifford (65).
REF – P Murphy (Carlow).