Monaghan lost by eight points to an impressive Offaly side in their All-Ireland qualifier at Tullamore.
Offaly led early on and Niall McNamee's 13th-minute goal into the top corner was just reward for their superiority.
Chris McGuinness' goal on 27 minutes helped Monaghan level the game but Offaly led 1-8 to 1-6 at half-time.
Offaly scored five unanswered points at the start of the second half and continued their domination to earn a deserved and comfortable victory.
Offaly recorded the first three points of the game, before Paul Finlay registered Monaghan's first score.
McNamee blasted the ball into the net to make it 1-3 to 0-1 but Monaghan made a mini-revival as Bernard O'Brien and Conor McManus played their part in McGuinness' goal.
The scores were level at 1-6 to 1-6 but Offaly then pulled away.
McNamee and Ciaran McManus starred for the home side in the second half.