They won the game at the Athletic Grounds in Armagh by 4-11 to 1-10.
Kieran Hughes scored for Monaghan before Tyrone responded with goals by Mark Donnelly and Stephen O'Neill late in the first half.
Ronan McNally was shown a red card for striking.
Donnelly scored his second just after the restart and when Dessie Mone was dismissed for two yellows, Peter Harte fired home a penalty to seal victory for the Red Hands.
Tyrone manager Mickey Harte said the game "turned on its head" just before half time.
"The conditions were difficult and Monaghan were setting the pace, playing against the breeze," he told UTV. "Their goal put them ahead and they looked comfortable.
"Getting a goal before half time was very important then they'd a man sent off so the world turned on its head as far as they were concerned.
"But sometimes when a team goes down a man they raise their game so we had to be careful.
"The best way to defend the lead was to attack and thankfully we did that and got the goal in the second half."