Mickey Harte’s side trailed by four points towards the end of a first-half which Cavan had bossed, but crucially scored 1-1 in injury-time, Plunkett Kane with the only goal of the game, to draw level at the break.
The Breffni Blues had Killian Brady sent-off after 49 minutes and Tyrone’s speed was too much.
Tyrone had eight different players on the scoresheet and outscored their opponents by ten points to three in the second-half.
Scorers for Cavan: M Dunne 0-4 (2f), E Keating 0-3, C Mackey 0-3, D Givney 0-1.
Scorers for Tyrone: K Coney 0-5 (2f), N Morgan 0-3 (3f), P Kane 1-0, P McNeice 0-3, S Cavanagh 0-1, M Donnelly 0-1, N McKenna 0-1, C McGinley 0-1.
CAVAN: A O’Mara; J Hayes, R Dunne, K Brady; D Barkey, J McLoughlin, J McEnroe; D McKiernan, D O’Reilly; M Reilly, N McDermott, M Argue; C Mackey (0-3), M Dunne (0-4, 2f), E Keating (0-3)
Subs: D Givney (0-1) for Barkey (46), N Smith for M Dunne (52), G McKiernan for D McKiernan (54), K Tierney for McDermott (62), M McKeever for Hayes (66), P Leddy for McLoughlin (70)
TYRONE: N Morgan (0-3, 3f); PJ Quinn, D McBride, R McKenna; R McNabb, D Carlin, T McCann; N McKenna (0-1), S Cavanagh (0-1); PJ Lavery, C Cavanagh, P Kane (1-0); P McNeice (0-3), M Donnelly (0-1), K Coney (0-5, 2f)
Subs: C Grugan for C Cavanagh (HT), C McGinley (0-1) for McNabb (48), A McCrory for McBride (54), E McKenna for Kane (57), S McGuigan for Lavery (67), P Hughes for Donnelly (67)
Referee: Martin McNally (Monaghan).