The home side were always in control after veteran Nicky Horan got them off to a bright start, with three early points and the first of two Eoin Marsh goals boosted them to a double scores interval lead, 1-11 to 0-7.
Marsh’s second goal came 10 minutes into the second period when soloing in before blasting to the net and substitute Derek Doran put his name on the third.
Roscommon grabbed a consolation goal to put a better complexion the scoreline, with David Dolan applying the finishing touch 10 minutes from the end.
Scorers for Meath: E Marsh 2-2, S Clynch 0-5 (1f, 1 65), N Horan 0-4 (3fs), D Doran 1-0, J Toher, R Massey, J Kelly, C Fitzsimons, K Keoghan 0-1 each.
Scorers for Roscommon: D Dolan 1-3 (1f), T Seale, K Conneely 0-2 each, M Kelly, CJ Coyne, G Fallon, B Kelly 0-1 each.
MEATH: S McGann; E Keogh, D Healy, C Reilly; J Toher, P Fagan, S Morris; S Clynch, S Donoghue; S Heavey, R Massey, N Kirby; N Horan, E Marsh, J Kelly.
Subs: K Keoghan for Massey (ht), D Doran for Kirby (43), C Fitzsimons for Donoghue (50), S Brennan for Keogh (57), P Durnin for Horan (64).
ROSCOMMON: D Dowd; S Curley, P Kelly, D Fallon; N Keenan, M Kelly, S Melia; T Seale, K Conneely; D Nolan, J Coyne, E Mulry; D Dolan, G Fallon, E Kenny.
Subs: R Lawlor for Mulry (31); D Flaherty for Melia, C Egan for Seale (both 49), B Kelly for Keenan (53).
Referee: O Elliott (Antrim).