Kevin Hughes came on to replace the injured Colm Cavanagh in a match played at a furious, intense pace.
Down fought back to level at 0-7 to 0-7 before Sean Cavanagh ended a spell of 16 minutes without a point for Tyrone to give his side a narrow half-time lead.
The teams traded second-half points until Down broke four points clear at 0-16 to 0-12.
Four McGuigan points brought the Red Hands level, the latter two coming after Down had been reduced to 14 men with the sending-off of Damien Rafferty for two yellow-card offences.
Points from McGuigan, Cavanagh, Philip Jordan and Colm McCullagh put Tyrone four clear at the start of extra-time but Down revived, getting to within two points when Coulter fisted the ball into the net.
Doyle added another point but Tyrone could only reply with a McCullagh point in the second period of extra-time.
DOWN 1-19 (A Rodgers 0-1, A Carr 0-4, L Doyle 0-6, D Gordon 0-1, P Murphy 0-1, J Clarke 0-1, D Hughes 0-1, B Coulter 1-3, K McKernan 0-1)
TYRONE 0-21 (C Cavanagh 0-4, S Cavanagh 0-4, R Mellon 0-1, C McCullagh 0-4, M Penrose 0-1, T McGuigan 0-6, P Jordan 0-1)
Tyrone: J Devine, R McMenamin, J McMahon, PJ Quinn, D Harte, C Gourley, P Jordan, C Gormley, R Mellon, B Dooher, B McGuigan, C Cavanagh, M Penrose, S Cavanagh, C McCullagh.
Down: B McVeigh, L Howard, D Gordon, D Rafferty, A Carr, L Doyle, P Murphy, J Lynch, A Rogers, J Fegan, R Murtagh, D Hughes, J Clarke, R Sexton, B Coulter.
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