Improving Tyrone are sunk by ace Meehan
Tyrone will face a relegation battle in good heart following an encouraging display at Pearse Stadium.
The Red Hands' best performance of the season to date just wasn't good enough to prevent Galway from stretching their unbeaten NFL run to three games, and a perfect seven wins from seven for new boss Liam Sammon.
Tyrone will take many positives from a hugely entertaining game in Salthill, where Galway full forward Michael Meehan proved the difference with a 1-5 tally.
The injury crisis is beginning to ease for Mickey Harte's side, but with just one point from their three games, results will have to improve soon.
Goals from Sean Cavanagh and Raymond Mulgrew put the Ulster men in a position to win an entertaining game that refused to submit to the wind and rain.
Meehan scored an early goal to give Galway a dream start, taking a pinpont pass from Padraic Joyce to beat Johnny Curran with a low shot.
The Red Hands trailed by 1-1 to 0-0 until they registered their first score midway through the half, but Sean Cavanagh's 17th minute goal sparked a rush, with 1-3 in the space of four minutes.
Cavanagh, making his first start of the season, collected Raymond Mulgrew's pass to blast the ball past Adrian Faherty.
Tyrone kept up the momentum, and scores followed from Ryan Mellon, Colm McCullagh and the lively Owen Mulligan for a 1-3 to 1-1 advantage by the 21st minute.
Galway were soon back on top, with Darren Mullahy and Matthew Clancy winning vital ball in around the half back area, and scores from Eddie Hoare, wing back Gary Sice and Meehan had them level on 1-4 each at the turnaround.
And they started the second half with another flourish - substitute Sean Armstrong scoring two delightful points, but Tyrone struck for a second goal through Mulgrew.
Both sides enjoyed periods of dominance, but it was Galway who always looked the more likely to succeed, even when a wonderful Mulligan point levelled the game again with 10 minutes to play.
The Tribesmen pushed home the advantage in the closing stages, with Sice and Coleman both putting over their second scores, and the brilliant Meehan bringing his tally for the day to 1-5, and a personal total of 2-28 from three games.
GALWAY: J Curran, PJ Quinn, C Gormley, M Swift, D Harte, D Carlin, R McMenamin, K Hughes, E McGinley, R Mellon (0-1), R Mulgrew (1-1), S Cavanagh (1-0), T McGuigan (0-2), C McCullagh (0-1), O Mulligan (0-3, 1 free). Subs: J McMahon for Carlin, N Gormley (0-1) for McCullagh, D McCaul for Swift.
TYRONE: A Faherty, D Finnegan, F Hanley, D Burke, G Sice (0-2) N Coyne, D Mullahy, P Geraghty, N Coleman (0-2), E Hoare (0-2), P Joyce, D Meehan, M Clancy, M Meehan (1-5, 3 frees), F Breathnach (0-1). Subs: S Armstrong (0-2) for Geraghty, C Bane for Breathnach, B Cullinane for Burke, Breathnach for Armstrong
Referee: A Mangan (Kerry).