Liam Bradley's side had recovered from an early two point deficit after scores from the Limerick duo of Killian Phair and Ian Ryan, with points from Paul McCann and Paddy Cunningham getting them back on terms.
Despite going behind again Antrim finished the half strongly with further points from McCann, Cunningham and Paddy McKeever edging the Saffrons into a 0-8 to 0-6 half time lead.
Antrim did suffer a blow in the first half when Justin Crozier was taken to hospital for a serious elbow injury, but were full value for their lead at the interval.
However the game changed dramatically early in the second half as the hosts conceded two penalties in quick succession, both of which were dispatched to the net by Ger Collins.
Cunningham did his best to keep the visitors in touch, but a late goal from Darragh Treacy sealed victory a 3-11 to 0-15 for Limerick, and saw Antrim become the third Ulster side to exit the Championship.