Galway recorded a facile victory in their first ever championship meeting with Louth, but needed the benefit of an injury time goal from substitute Noel Meehan to secure a 2-08 to 0-09 success at Parnell Park.
Louth's finishing proved less than clinical as they missed a number of chances, hitting five consecutive wides just after Padraig Joyce had breached their cover for the first Galway goal on 16 minutes.
An even start saw Matthew Clancy pop over a quick point, followed by scores from Louth attackers JP Rooney and Mark Stanfield, the second a crisp shot from the sideline after 7 minutes.
Joyce levelled at 0-02 apiece with a 20-metre free and bagged another two, while Paudie Mallon was booked.
Donnellan then put the Tribesmen three points clear with his first from 40 metres.
The goal showed all of Galway's attacking class, as Joyce raced 20 metres clear of the Louth cover and drilled the ball into Shane McCoy's net.
Two Stanfield frees and a point from midfielder Paddy Keenan from 45 metres kept Louth in touch at 0-05 to 1-05 down at the break.
Mark Stanfield converted two frees after the restart, but with Louth having to wait until the hour when JP Rooney and half forward Nicky McDonnell added further scores, there was only going to be one winner.
Noel Meehan made sure of Galway's advancement with a well-finished goal, set up by the quick thinking of another substitute John Devane.
Scorers: Galway: P Joyce 1-03 (2f), N Meehan 1-00, D Savage, M Donnellan 0-02 each, M Clancy 0-01 Louth: M Stanfield 0-05 (5f), JP Rooney 0-02, P Keenan, N McDonnell 0-01 each
Galway: B Donohue, K Fitzgerald, B Dooney, D Meehan; P Clancy, T Meehan, G Fahy, K Walsh, S O Domhnaill; J Bergin, M Donnellan, M Clancy; D Savage, P Joyce, T Joyce
Subs used: N Meehan for T Joyce (ht), J Devane for Clancy (66 mins)
Louth: S McCoy; A Page, P Mallon, J Carr, D Shevlin, S Gerrard, R Rooney, D Devaney, P Keenan, N McDonnell, O McDonnell, R Finnegan; A Hoey, M Stanfield, JP Rooney
Subs used: D Burke for R Rooney (51 mins), D Clarke for McDonnell (61 mins), P Matthews for Devaney (69 mins), R Kenny for Stanfield (70 mins)
Filed by Barry McEneaney