Monaghan kept hold of top spot in NFL Division 2 thanks to Paul Finlay's injury-time point at Parnell Park.
Dublin, who had both Mark Vaughan and Bryan Cullen sent-off, battled their way into a 1-10 to 0-09 lead before Finlay and Thomas Freeman, between them, shot the game's final four scores to seal a draw.
Freeman hit four frees as the wind-backed visitors led 0-06 to 0-03 at half-time.
Paul Flynn's goal and points from Bernard Brogan and Conal Keaney had Dublin ahead but Monaghan rallied late on to maintain their unbeaten run in this season's league.
Both sides came into this game, which was re-fixed after the bad weather forced a postponement last weekend, with three wins behind them.
However, the football in the first half left a lot to be desired with Jason Sherlock's effort after only 14 seconds being the only score from play.
Referee Syl Doyle's whistle peppered the Donnycarney air all too often with the opening 35 minutes being blighted by frees, injury stoppages and a good deal of niggle.
Mark Vaughan kicked a third-minute free to double Dublin's lead but two Freeman frees, with a Finlay point sandwiched in between, had the Farney men leading by 0-03 to 0-02.
Vaughan, who earned his first yellow card for a foul on Conor McManus, stepped up to level the game with a 15th-minute free.
But, aided by the wind, Monaghan pulled clear again thanks to three more successful placed balls from Freeman (0-02) and Finlay.
Dublin only had themselves to blame as their attacking unit struggled to maintain possession and, by the interval, the Leinster champions had shot six wides including three missed frees from Vaughan (2) and Keaney.
The tension bubbled over on the restart with the action pock-marked by a series of off-the-ball incidents.
Vaughan saw yellow for the second time when he caught Freeman with an elbow as the Monaghan marksman tried to dash by him.
Monaghan moved five points clear when Finlay added to his tally and a score from a narrow angle from substitute Stephen Gollogly - the Ulster side's only point from play in the entire game - heaped further pressure on 14-man Dublin.
The men from capital were clearly equal to it as within three minutes they were back level.
David Henry raided forward from his defensive station to slot a morale-boosting point and begin a terrific 15-minute spell for Dublin, during which they scored 1-05 without reply.
Moments later, they had the ball in the Monaghan net as Paul Flynn rose highest to claim a high ball and he then got free to accept a Sherlock pass and left-foot home past goalkeeper Padraig McBennett from 14 metres out.
Points followed from Bernard Brogan and Keaney and with the workaholic Shane Ryan beginning to sew up the midfield sector, the Dubs looked poised for the win.
They might have had a second goal in the 52nd-minute but Bernard Brogan, who should have shot himself, decided to try and put Sherlock through and the move broke down.
Keaney landed his fourth point of the afternoon to put four between the sides with little over five minutes of normal time remaining.
Monaghan needed inspiration from somewhere and unsurprisingly, it came from their free-taking duo.
Finlay's fourth successful free and another from Freeman cut the gap to two points with three minutes to go.
The Farney men almost hit the front a minute later when Freeman, the Ulster Footballer of the Year, drove forward and forced Dublin net minder Stephen Cluxton into an excellent save.
The Dubs' defence was struggling to cope with the pace of Freeman and after the corner forward landed a 71st-minute point, putting the minimum between the sides, he was fouled by Derek Murray for Finlay's equaliser.
Finlay pointed from 25 metres out and Dublin had to finish the game with only 13 players after Bryan Cullen was dismissed for his second bookable offence, as he rugby-tackled an opponent to the ground.
Scorers:
DUBLIN: C Keaney 0-04 (0-01 '45', 0-01f), P Flynn 1-00, M Vaughan (0-02f), B Brogan (0-02f) 0-02 each, J Sherlock, D Henry 0-01 each.
MONAGHAN: T Freeman 0-07 (0-07f), P Finlay 0-05 (0-05f), S Gollogly 0-01.
