Down had five points to spare over Galway after a 2-11 to 1-09 win in their Allianz Football League Division 1 clash in Newry.
Galway put in a spirited showing but Peter Fitzpatrick's injury-time goal confirmed Down's win in Newry on Sunday afternoon.
It was an important victory for James McCartan's side ahead of next Saturday's Ulster derby against Armagh.
The result may not have gone Galway's way, but under-fire manager Tomas O Flatharta will have been pleased by the competitiveness of his side.
Now without retired joint-captain Kieran Fitzgerald and Niall Coleman, who has withdrawn from the panel, O Flatharta is also currently missing the services of Padraic Joyce, Michael Meehan and Nicky Joyce.
Colin Forde, David Reilly and Joe Bergin started for the westerners at Pairc Esler, with Padraig Lally and Paul Conroy both late inclusions in goal and at midfield respectively. Conor Laverty replaced Paul McComiskey in the Down attack.
The hosts got off to a sluggish start and were 0-03 to 0-00 behind inside seven minutes. Down reduced the arrears to 0-05 to 0-03 by the 21st minute, with Marty Clarke, Mark Poland and Laverty splitting the posts.
Corner forward Laverty failed to find the target when presented with a goal-scoring opportunity by Benny Coulter. He rushed his effort, flicking it wide off the outside of his boot.
On the approach to half-time, Down began to dominate the play. Points from play from Danny Hughes and Laverty got them level, before the latter raced through and passed for Fitzpatrick who set up Maginn for his 29th minute goal.
Clancy replied for Galway, but well-taken frees from Clarke and Poland gave Down a four-point buffer at the interval.
McCartan's charges played in fits and starts in their league opener against Mayo and they were guilty of taking too much out of the ball and not putting Galway away after the break.
Sloppy passing blighted the game at times, and Down could have been far more clinical. A case in point was when Laverty was whistled up for taking too many steps before Marty Clarke found the net.
Galway had second half points from Armstrong (0-02) and Joe Bergin, but it was a 59th minute goal from defender Gary O'Donnell that kept them in the hunt.
Points from Declan Rooney and Peter Fitzpatrick pushed Down's lead out to 1-10 to 0-08. But when the home defence failed to cope with a long ball and David Reilly played in fellow wing back O'Donnell, goalkeeper Brendan McVeigh was beaten by a brilliant finish from the Tuam Stars clubman.
McCartan sent on Aidan Carr, McComiskey and Liam Doyle and the fresh legs helped Down see out their maiden victory in Allianz NFL Division 1.
McComiskey stretched the lead back to three points, and it was his run and hand pass that created Fitzpatrick's late goal. The busy midfielder managed to dive and fist the ball home, giving the final scoreline a flattering look.
