Tyrone boss Micky Harte will gear his side up for one more game as they bid to reach the new Super 8s this season in the All Ireland Championship qualifiers.
The Red Hands suppressed a stubborn second-half recovery by Cavan to claim an 0-18 to 1-12 success.
Martin Reilly’s goal inspired Cavan to draw level from five points adrift but Ronan O’Neill’s four points off the bench eased Mickey Harte’s men through.
Cavan contributed to an end-to-end second half but finished with 14 men after Ciaran Brady’s second booking.
Harte said: “It’s always a battle in these qualifiers, you’re never sure how it’s going to go and you don’t know what way the team that you’re playing is going to come and kick into life.
“In the first-half we wore them down, we got a decent lead of 0-9 to 0-5 and then getting the point at the start of the second half to go to double scores, I thought this job is fairly well under control here but we let it slip.”
“This is a winner take all situation because you don’t have any more chances, we gave up our second chance the day Monaghan beat us.
“This is the last chance saloon and it’s good to have players that can come through that and show they have the required steel to deal with tense situations.”
Cavan manager Mattie McGleenan: “The effort that they gave was just fantastic and the game was still there at the death and that’s all you can ask of any player.”
Tyrone will now meet Cork in the fourth round due to be played this weekend.
A win will see the Red Hands go into Group Two of the Super Eights along with Dublin, Donegal and the winner of the qualifier between Armagh or Roscommon.