Two first-half goals by Peter Harte made the difference for Tyrone in a rain-sodden clash at Casement Park.
His first maximum, in the sixth minute, followed a hectic period of play. First, Antrim 'keeper Chris Kerr, in his attempt to clear it, gave the ball away to Darren McCurry, but Kerr smothered the corner-forward's attempt to net.
Then Paul Doherty gifted a chance to Harte, who blocked the ball home to put the visitors 1-1 to 0-0 ahead. The Tyrone cheers still hadn't died down when Antrim cracked home a goal of their own.
Justin Crozier scythed through the Tyrone defence and found Kevin Niblock. He was hauled down and fired home the resultant penalty-kick in the seventh minute.
The teams were level at 1-3 each on 22 minutes, but a flurry of points from new boy McCurry and Plunkett Kane left Tyrone leading by 2-6 to 1-4 at the break.
Edendork lad McCurry was a thorn in Antrim's side as he notched five points from play and made a strong claim for a permanent place in the Red Hands team.
Antrim didn't score from the 37th until the 55th minute, by which time Tyrone had sped 2-10 to 1-5 ahead, before finishing six-point winners with a place in the semi-finals secured.
SCORERS – Tyrone: P Harte 2-0, D McCurry 0-5, R McNamee, P Kane 0-2 each, S Cavanagh, S O'Neill (f), J Laverty, N Morgan ('45') 0-1 each. Antrim: C Fleming 0-3 (3f), K Niblock 1-0 (pen), P Cunningham 0-2, T Scullion, J Crozier, S McVeigh, M Herron, C Murray 0-1 each.
TYRONE – N Morgan; A McCrory, C McCarron, D McNally; R McNamee, C Gormley, S Warnock; P Kane, S Cavanagh; T McCann, P Harte, P McNiece; D McCurry, S O'Neill, C McAliskey. Subs: D Carlin for Gormley (26), M Donnelly for McNiece (h-t), J Laverty for Harte (44), Joe McMahon for O'Neill (53), M Donnelly for Carlin (62).
ANTRIM – C Kerr; K O'Boyle, P Doherty, S Finch; T Scullion, D McCann, J Crozier; S McVeigh, S McCarron; C Murray, K Niblock, C Fleming; M McCann, M Herron, M Pollock. Subs: J Laverty for D McCann (h-t), B Herron for Fleming (47), R Murray for Pollock (49), P Cunningham for Niblock (55), P McNicholl for Doherty (66).
REF – C Brannigan (Down).