Cavan made it two wins from their opening two Division Three matches with a comfortable victory over Offaly in Tullamore on Sunday.
Martin Dunne slotted over four points in first half while Eugene Keating scored two as the Ulster team went in 0-9 to 0-5 ahead at half-time.
Cavan's lead was never threatened and Keating netted the game's only goal to seal the victory.
The Breffni men are joint leaders on four points with Roscommon.
Cavan made a superb start, holding a 0-7 to 0-0 advantage after 23 minutes and it could have been more.
Kevin Tierney shot over with a goal chance on offer while Meath keeper Alan Mulhall kept out Niall McDermott's effort.
Offaly finally registered a point through Niall McNamee and they had reduced the gap to four by the break.
The goal came early in the second half with Dunne setting up Keating to net and put Monaghan seven points in front.
Allianz Football League results
Tyrone 2-15 0-15 Mayo
Kerry 0-14 0-16 Derry
Cork 0-16 1-12 Kildare
Westmeath 1-7 0-14 Dublin
Galway 0-12 1-16 Donegal
Monaghan 0-20 0-8 Meath
Louth 0-11 2-8 Laois
Roscommon 1-16 1-9 Wexford
Limerick 2-11 0-11 Longford
Offaly 0-8 1-11 Cavan
Antrim 1-13 3-9 Wicklow
Clare 0-11 1-8 Leitrim
Tipperary 0-12 1-9 Waterford
Interprovincial Hurling semi-finals
Connacht 1-18 0-16 Munster
Leinster 8-18 1-21 Ulster