Mickey Harte's side won the game thanks to Stephen O'Neill's penalty, virtually the last kick of the game.
The result means it is two wins out of two for Tyrone in the League.
Derry earned their first win, 1-17 to 2-11 over Laois in Division Two.
However, it took a strong comeback for the win. Ross Munnelly and Damien O'Connor scored goals as Laois took a commanding 2-7 to 9 points lead into the half-time interval.
Derry fired over three points in the second period and they took a decisive step towards victory with Emmett McGuckin's goal. The Oak Leaf county held on despite James Kielt's dismissal.
Elsewhere, Antrim had a miserable day, ending with 13 players as they went down 1-12 to 13 points to Sligo.
Pat Hughes's goal helped Sligo into a 1-8 to 0-04 half-time lead but Antrim notched five unanswered second half points. Kevin Niblock and Michael Magill were sent off late on as Sligo held on for the win.
Armagh's match with Wexford was postponed due to a waterlogged pitch.
Meanwhile, on Saturday, Donegal defeated Down 12 points to 7 in Division One in Ballybofey.
Down had led by three points thanks to some poor Donegal finishing in the first half.
Michael Murphy of Donegal sent over the first score of the game, but with wides mounting, Down capitalised, Donal O'Hare slotting over four points, three from frees and McKernan scored from long range.
Donegal were looking sharp in the second half with Murphy scoring three points, Rory Kavanagh, Leo McLoone, Ross Wherrity and Declan Walsh finiding the target.
O'Hare found Down's sixth point with McKernan also scoring.
However, Daniel McLaughlin's score saw Donegal seal the success.
Cavan beat Monaghan1-10 0-5 in a Division Three derby which saw five players being sent off.
Monaghan forward Conor McManus was red-carded first, Cavan's Martin Dunne's dismissal came shortly after.
Cavan led at half time - but John McCutcheon's dismissal for a high tackle brought them down to 13 men.
Next to go were Monaghan pair Davin Doogan and Dessie Mone for two yellow cards.