Conor McManus hit 12 points but Monaghan still contrived to end up on the losing side as Dublin snatched a 1-14 to 0-16 Division 1 win.
Monaghan hit five unanswered points in four minutes to move into a 0-7 to 0-2 lead but Dean Rock's six points helped the Dubs lead 0-10 to 0-9 at half-time.
A Diarmuid Connolly penalty extended Dublin's lead to 1-11 to 0-9.
McManus struck seven of the next eight scores to put Monaghan ahead but Dublin hit the final two scores to win.
Cormac Costello's 67th-minute point brought the sides level and substitute Bernard Brogan's injury-time score earned the Dubs a fortunate victory.
Both teams went into the game on a maximum four points and after the sides were level at 0-2 to 0-2, Monaghan struck a quickfire five straight scores with Owen Duffy and the Hughes brothers Darren and Kieran also on target for the Farney men.
However, Dublin outscored Monaghan 0-8 to 0-2 during the remainder of the first half as indiscipline allowed Rock to fire over a series of frees as Paddy Andrews started to win his battle with Colin Walshe.
Monaghan suffered a blow before the break as Kieran Hughes had to be carried off with an apparent leg injury.
The Dubs looked in control early in the second half as Connolly netted his penalty to increase their lead to 1-11 to 0-9 after Paul Flynn had been fouled.
However, instead of pushing on, the Dubs' play began to become increasingly laboured four straight McManus frees cut the margin to a single point with 15 minutes remaining.
Flynn's 58th-minute point doubled Dublin's lead but Monaghan were ahead in the 66th minute helped by three more McManus points - including his fourth effort from play.
But as Monaghan then appeared to make the mistake of looking for the finishing line, Cormac Costello's second point levelled the contest before sub Brogan kicked what proved to be the winning score in the first minute of injury-time.
Fintan Kelly appeared to be working the ball towards an equalising chance for Monaghan a minute later but was off-target with his over-ambitious effort.
ALLIANZ FOOTBALL LEAGUE FIXTURES/RESULTS
Dublin 1-14 0-16 Monaghan
Armagh 1-10 0-12 Fermanagh
Sunday - 14:00 GMT (unless stated)
Cork v Roscommon, Pairc Ui Rinn
Donegal v Mayo, Ballybofey
Down v Kerry, Pairc Esler
Derry v Galway, Celtic Park
Laois v Tyrone, O'Moore Park
Meath v Cavan, Pairc Tailteann
Longford v Kildare, Pearse Park
Offaly v Sligo, Tullamore
Westmeath v Tipperary, Mullingar
Limerick v Clare, Newcastlewest
Wexford v London, Wexford Park, 13:00
Antrim v Leitrim, Corrigan Park
Carlow v Waterford, Dr Cullen Park
Louth v Wicklow, Gaelic Grounds