Tyrone's fifth straight win was enough to secure Mickey Harte's men promotion with two matches still to play in the Division Two campaign.
Peter Harte got the goal with a penalty in the second half as Tyrone maintained their 100% league record.
A foul on Harte had led to the penalty and he found the net despite keeper Adrian Faherty getting a hand to it.
Tyrone's P J Quinn was shown a straight red card after Galway's Padraig Joyce went to ground.
But it did not matter as Tyrone, boosted by three Kyle Coney points in two minutes, were always too strong for the home side at Tuam Stadium.
"Whoever got a goal was always going to be in a strong position and fortunately it was us," said Red Hands manager Mickey Harte.
"It was a crucial score and, although Peter was the man fouled, he had the confidence to take it."
Tyrone are now certain to finish in the top two as Kildare are the only team who can possibly match their 10 points.