Peter Harte scored both the Tyrone goals in the first half - the first after a defensive mix up and the second a fine individual effort.
Kevin Niblock replied for the Saffrons with a penalty after a foul in the square as Tyrone led 2-6 to 1-4 at the break.
"Antrim made it hard for us especially in the first half and our goals maybe came slightly against the run of play," Red Hands manager Mickey Harte told UTV.
All Ireland champions Donegal again fielded a young side and they went down to their second consecutive defeat losing 3-16 to 1-5 against Monaghan in Ballybofey.
Keith McEnaney, Dermot Malone and Darren Hughes got the Monaghan goals with Adrian Hanlon replying for Donegal.
Shane McCabe and Shane Ward got the goals for Fermanagh in their 2-15 to 1-5 win over St Mary's University College at Brewster Park.
On Saturday night Cavan defeated Armagh 3-9 to 1-11 at the Athletic grounds and Derry overcame UUJ 1-14 to 0-6 at Celtic Park.