The home side suffered an early blow when their county senior forward Eamon Wallace hobbled off after 10 minutes. It took them until the end of the opening quarter to get on the board with a pointed free from Bryan McMahon.
However, they settled into the game thereafter and finished the first half with a flourish as Joey Wallace, younger brother of Eamon, fired to the net to leave it 1-4 to 0-4 at the break.
There was little between the sides for most of the second period before five unanswered points in the closing stages saw Meath comfortably through.
The Royals can now look forward to meeting Offaly in a semi-final tussle at Parnell Park on Wednesday next.
Scorers for Meath: B McMahon 0-6, 4fs, S Mattimoe 0-5, 2fs, J Wallace 1-0, N Shortall, B Dardis 0-1.
Scorers for Louth: R Burns 0-6, 5fs, C Grimes 0-3, C Doyle 0-1.
MEATH: A Colgan; S Carty, C McGill, D McQuillan; B Power, S Melia, S McEntee; C Sheridan, A Flanagan; N Shortall, B O’Brien, P Harnan; E Wallace, B McMahon, J Wallace.
Subs: S Mattimoe for E Wallace (10), H Rooney for Sheridan (42), C Finn for Power (51), B Dardis for J Wallace (59).
LOUTH: N Cooney; E Lafferty, D Campbell, K Lenaghan; D McMahon, P Reilly, S Thornton; D Brodigan, W Campbell; R Quigley, J Stewart, C McKeever; C Doyle, C Grimes, R Burns.
Subs: R Curran for Thornton (18), C Ward for Brodigan (black card, 43), R Carr for McKeever (51), K Harty for Doyle (60).
Referee: G Whelan (Wicklow).