Peter Harte drilled home a 25th-minute penalty, with Sean Cavanagh scoring twice as the Red Hands built up a 1-5 to 0-03 interval lead.
Aidan Carr netted a Down penalty, before Darren McCurry drilled home a Tyrone goal, but Down responded with two quick-fire goals from Donal O’Hare and Conor Maginn.
It was Sean Cavanagh who kicked a stoppage time free to rescue a replay for Tyrone, who led by seven at one stage.
Goalkeeper Niall Morgan landed a long range free, and Sean Cavanagh skipped through for a score, before Donal O’Hare opened the Down account from a free.
Tyrone struggled to find the range with a greasy ball, Ciaran McGinley and Mattie Donnelly both missing the target with decent opportunities.
Darren McCurry and Cavanagh knocked over frees, but Tyrone were almost caught on the breakaway.
It was Morgan who came to the rescue, dashing off his line to intercept on the 20 metre line as Conor Laverty attempted to release Niall Madine.
But Tyrone struck for a goal in the 25th minute. Mark Donnelly collected Cavanagh’s dropping sideline kick, and managed to poke the ball to the net despite being held back.
Referee David Coldrick, rather than play the advantage rule and allow the goal, called play back for a penalty, which Peter Harte smashed to the net.
The home side managed just two points from play in that first half, and hit nine wides, before taking a 1-5 to 0-3 lead into the interval.
Down manager James McCartan performed major surgery on his side, making a triple substitution at half-time, including the introduction of Benny Coulter, who surprisingly lined out at midfield.
Another of those subs, Jerome Johnson, made an immediate impact, winning a penalty which also earned Morgan a black card in the 39th minute.
Substitute ‘keeper Mickey O’Neill faced up to Aidan Carr’s kick, but had no chance with a bullet which almost ripped the net off at the Gortin Road end.
But Kyle Coney delivered a defiant response with two delightful points, before another Down replacement, Johnson’s younger brother Ryan, sent Madine in for a point.
The game exploded into life with three goals in the space of four minutes early in the final quarter.
Stephen O’Neill, in as a sub for his first appearance this year, played a key role in the flowing move which ended with Darren McCurry rifling his shot past Brendan McVeigh.
But Down’s response was devastating. With Kevin McKernan driving their challenge and Ryan Johnson tormenting the Tyrone defence, they stunned their hosts with two goals in the space of three minutes.
Johnson sent Donal O’Hare in to finish past sub ‘keeper O’Neill, and three minutes later, Conor Laverty slipped the ball to Conor Maginn for a superb goal.
Mark Poland gave Down the lead for the first time on 61 minutes, and Coulter stretched the advantage.
But skipper Cavanagh rescued the Red Hands, winning and converting two late frees to send the teams back to Newry for the rematch.
Tyrone: N Morgan (0-01, f), A McCrory, D McBride, B Tierney, T McCann, Mattie Donnelly, P Harte (1-00, pen), C Cavanagh, C Clarke, Mark Donnelly, S Cavanagh (0-05, 3f), C McGinley, D McCurry (1-02, 0-2f), N McKenna, K Coney (0-3).
Subs: R McKenna for McCann, M O’Neill for Morgan (BC), S O’Neill for N McKenna, J McMahon for McBride, C Gormley for Tierney, M Penrose for McGinley
Down: B McVeigh, D McCartan, B McArdle, R Boyle, D Rooney, A Carr (1-00, pen), C Garvey (0-1), P Turley, A Rogers (0-01), C Maginn (1-00), M Poland (0-1), K McKernan, D O’Hare (1-02, 0-2f), N Madine (0-01), C Laverty (0-01).
Subs: R Johnson for Boyle, B Coulter (0-01) for Turley, J Johnson for Rogers, L Doyle for J Johnson, D Turley for Garvey, P Devlin for Maginn (BC)
Referee: D Coldrick (Meath).