The teams went into the interval level at seven points apiece but Conor McAliskey scored the only goal of the game late on to secure a 1-14 to 0-15 win for Mickey Harte's side.
Sean Cavanagh top scored with seven points for Tyrone, five of which came from frees.
Down also were made to work hard for their 1-11 to 0-12 win in Cavan.
Paul McComiskey's early goal put James McCartan's side in the ascendancy but the sides were level at the break, 1-5 to 0-8.
Cavan nudged ahead in the second half but late points from Liam Doyle and Ryan Kelly clinched Down victory.
Elsewhere Monaghan were 1-13 to 2-6 winners over St Mary's at Clones while Frank Dawson got a debut win as new Antrim manager as the Saffrons defeated UUJ 1-15 to 2-9.
Kevin O'Boyle scored the Antrim goal to give the former Down hurling and Burren football manager an early boost after his first competitive game in charge.
Power NI Dr McKenna Cup Results:
- Cavan 0-12 Down 1-11
- Tyrone 1-14 Derry 0-15
- Monaghan 1-13 St Mary's 2-7
- Antrim 1-15 UUJ 2-9