Monaghan maintained their winning start to Division One of the Football League as Down were left to rue several missed chances in their 0-13 to 0-11 defeat.
Down led 0-2 to 0-0 and 0-5 to 0-2 but Monaghan hit seven of the next eight scores to lead 0-9 to 0-6 at half-time.
Monaghan looked set for a comfortable win as they moved five ahead but Down fought back in the final quarter.
Seven minutes of injury-time gave Down chances to at least get on terms but errant shooting cost the Mournemen.
Down's performance at Clones was a big improvement on last week's opening 3-15 to 0-7 thumping by Donegal but a second defeat leaves Eamonn Burns' side facing the relegation battle that most pundits predicted.
The Mournemen hit the opening two scores with Connaire Harrison and Darragh O'Hanlon on target and while points from Dermot Malone and Shane Carey helped Monaghan level, three more Harrison points put Down 0-5 to 0-2 ahead by the 15th minute.
However, Down then lost their way as Monaghan began to run through the Mourne defence with a number of poor kick-outs by keeper Stephen Kane not helping the visitors' cause.
Kane was lucky not to concede a goal in the 22nd minute as he lost possession after soloing some 35 yards from his goal with Conor McManus' lobbed effort towards the empty net bouncing over the crossbar for a point.
That point levelled the contest and further scores from Thomas Kerr, the lively Malone, Owen Duffy and Fintan Kelly helped the Farney men lead 0-9 to 0-6 the break.
Down were robbed of playmaker Mark Poland as he took a heavy hit straight after the restart and Monaghan looked in control when Shane Carey and Ryan McAnespie pointed to increase their lead to five.
The lead was still five (0-12 to 0-7) in the 53st minute but after Kane made a great save to deny a Darren Hughes goal chance, Down fought back in the closing stages to leave the home side hanging on.
Down may look back on their ninth point with regret as substitute Packie Downey's goal attempt skimmed over the crossbar after Drew Wylie had lost possession.
Daniel McKenna's 64th-minute point appeared to have given Monaghan some breathing space but the seven minutes of injury time gave Down enough opportunities to take something out of the game.
Points from Downey and Harrison left the scoreline at 0-13 to 0-11 with five minutes left but Harrison's free-kick miss from 21 metres two minutes later sealed Down's fate.
WEEKEND ALLIANZ FOOTBALL LEAGUE RESULTS
Mayo 0-07 0-09 Dublin
Armagh 0-15 1-13 Laois
Cavan 1-11 1-12 Derry
London 1-11 4-04 Carlow
Donegal 2-14 1-07 Cork
Kerry 1-10 0-14 Roscommon
Monaghan 0-13 0-11 Down
Fermanagh 0-10 0-06 Meath
Galway 1-09 1-11 Tyrone
Kildare 1-12 1-08 Offaly
Longford 0-13 1-08 Limerick
Sligo 1-11 1-10 Westmeath
Tipperary 2-07 1-07 Clare
Antrim 1-08 0-07 Wexford
Leitrim 1-06 0-10 Wicklow
Waterford 1-09 1-10 Louth