Monaghan hit the front towards the break and led 0-8 to 0-7 at half time.
Dermot Malone scored the games only goal as Tyrone went close to forcing a replay.
After the game Tyrone manager Micky Harte remonstrated with the referee for not playing enough added time at the end.
Tyrone will now meet Louth in the first round of the qualifiers while Monaghan take on Armagh in the Ulster Semi Final.
Conor McAliskey gave his reaction to the defeat to Pauric Hilferty afterwards.