Westmeath manager Pat Flanagan said: “I can’t say enough about the players. They have taken a lot of stick over the past couple of weeks but they are great lads and they have put in a huge effort.
“To come out and score three points in the last five minutes was absolutely brilliant.”
Galway looked set for victory when they led by two points with three minutes of normal time left but they lost it at the death.
“We got into a very good position where we were two points up and we just couldn’t hold on and we gave them the last three points of the game,” said Galway manager Alan Mullholland. “We are a team in transition and we can’t expect to beat anyone. We have to earn our victory so we will just have to bounce back against Meath next week.”
Westmeath, who were rank outsiders ahead of the game, turned in a good first-half performance playing against a strong wind went in level at half-time, 0-6 each.
Indeed, Westmeath missed a glorious goal opportunity when Ger Egan punched wide from close range, while at the opposite end Westmeath keeper Gary Connaughton produced an outstanding save to deny Danny Cummins in first-half stoppage time.
The sides were level on three more occasions in the second half with Danny Cummins’ point in the 57th minute levelling matters at 0-11 each, although the Galway man should really have found the net.
However, points from substitute Sean Armstrong and Paul Conroy looked to have given Galway the win when they led 0-13 to 0-11 with seven minutes to play.
But Westmeath substitute Denis Glennon raced through to score a point, before a John Heslin free levelled matters with three minutes of added time left.
At the death, a long delivery by Kevin Maguire was laid off by Denis Glennon into Paul Bannon, who sent over the winning point with the last kick of the game.
Scorers for Westmeath: J Heslin 0-7 (7f), P Sheridan, David Glennon, Paul Sharry, G Egan, C McCormack, Denis Glennon, P Bannon 0-1 each.
Scorers for Galway: M Martin 0-4 (4f), P Conroy, D Cummins 0-2 each, M Hehir (1f), C Doherty, N Coleman, K McGrath, S Armstrong 0-1 each.
WESTMEATH: G Connaughton; M Curley, K Gavin, K Maguire; D McDermott, P Sharry, A Finnan; J Heslin, P Bannon; K Martin, G Egan, P Sheridan; A Giles, M Ennis, P Sharry.
Subs: C McCormack for Sheridan (55), Denis Glennon for Giles (56).
GALWAY: M Breathnach; K McGrath, F Hanley, K Kelly; G Bradshaw, J Dunne, G Sice; N Coleman, J Bergin; C Doherty, P Conroy, M Hehir; M Martin, N Joyce, D Cummins.
Subs: D Burke for Joyce (h-t), G Higgins for Martin (48), S Armstrong for Hehir (49), G O’Donnell for Bergin (57).
Referee: D Gough (Meath).