Goals in either half proved the difference as Monaghan were made to fight all the way at the Queen's Arena.
Seamus McGarry's haul of eight points - seven from play - was not enough for Antrim.
In a helter-skelter first half, Odhran Eastwood's free put Antrim ahead before McGarry (2) exchanged points with Michael Brannigan and David Garland.
Dermot Gleeson blasted in a goal to put the Farney men in front but Antrim responded well, hitting four of the next five points. Monaghan took the lead again but lost midfielder James Mealiff to a black card, with Eastwood kicking the resulting free to leave the sides level at the break, 1-6 to 0-9.
It was nip and tuck in the second half until Monaghan hit the crucial score on 45 minutes when Brannigan fed David Garland who swivelled and fired low to the net to make it 2-9 to 0-13.
Antrim responded with points from Ruairi Scott and McGarry, but the snap was fading from their challenge, and Monaghan pulled away with scores from Barry Kerr (two), Garland, Stephen Finnegan and David McAllister.
Scorers - Monaghan: D Garland 1-3; M Brannigan 0-4 (1f); D Gleeson 1-1; B Kerr 0-2; D McAllister, S Finnegan, F Hanratty, M Tierney 0-1 each. Antrim: S McGarry 0-8 (1f); O Eastwood 0-4fs; R McCann, R Scott, P Healy, P McCormick 0-1 each. MONAGHAN - S Garland; C Lennon, M Murnaghan, J Daly; N Kearns, J Mealiff, Finnegan; S Woods, D McAllister; B Kerr, F Maguire, S McCabe; D Gleeson, M Bannigan, D Garland. Subs: F Hanratty for Daly (22), P Flynn for Mealiff (30), M Tierney for McCabe (33), R McDonald for Maguire (52), J Walshe for Woods (59). ANTRIM - A Hasson; P Brannigan, T McGoran, McCormick; R Hannigan, P Healy, E Walsh; D Nugent, R Delargy; S McGarry, C Small, J McAuley; O Eastwood, R McCann, R Scott. Subs: C Lyttle for Hannigan (49), E Fyfe for McAuley (53), P Treanor for Scott (56). REF - M Farrelly (Cavan)