Despite dominating the game for long periods, it looked as though Ian Foster’s men would have to settle for a share of the spoils, after twice allowing the Tribesmen back into the game.
However, the towering centre-half clinched a deserved win in the 87th minute, climbing highest to head home a Daniel Kearns corner.
The Louth men wasted countless chances but deservedly hit the front on 18 minutes when Mark Quigley hit a stunning 30-yard free kick to the top left-hand corner of the net, giving Greg Fleming no chance.
However, that lead lasted just three minutes as Joseph Yoffe levelled from the penalty spot after Ross Gaynor clumsily fouled former team-mate Shaun Kelly inside the area.
Dundalk had plenty of chances to restore their lead after that and eventually did so on 71 minutes, when Jason Byrne headed home from eight yards out.
However, after Quigley had squandered a glorious chance when he hit the post after rounding Fleming, Galway levelled through Seán Kelly’s cool finish from the edge of the box.
That looked enough to earn Sean Connor’s men a share of the spoils until Guthrie popped up with his late intervention to get the Lilywhites off the mark for the campaign.
DUNDALK: P Murphy; Madden, Hawkins, Guthrie, N Murphy; Kearns, Bennett (Maher, 45 mins), Quigley, Ward, Gaynor; Byrne.
GALWAY UNITED: Fleming; Shaun Kelly, Sinnott, Maher, Walsh; Ryan (Cash, 59 mins), Sean Kelly, G Curran, Moore; Yoffe (Murphy, 67 mins), Feeney (E Curran, 81 mins).
Referee: P Tuite (Dublin).