Antrim had suffered losses against Wexford, Kilkenny and Dublin heading into the game in Salthill, but made a bright start as Joe McLaughlin scored their first two points.
Conor Whelan responded with two for Galway before Niall O’Connor and Conor Cooney traded scores.
The Tribesmen then rattled off three successive points to go ahead for the first time, but Antrim reduced the gap to one point.
Monaghan and Cooney re-established Galway’s advantage before Antrim stopper Ryan Elliot thwarted Concannon’s goal attempt.
Cooney and McLaughlin exchanged two more frees each and Concannon rifled home a goal on 29 minutes.
Paddy Burke fouled Whelan, but the referee opted to play the advantage and Concannon was not to be denied twice in quick succession.
Cooney tagged on some more frees with Burns then finishing low to net a second goal in first-half stoppage time.
Things went from bad to worse for the Saffrons, who hit seven wides in the first half, as Declan McCloskey was shown a controversial straight red card for grappling.
Cooney stroked over his seventh free of the first half to give Galway an 11-point advantage at the break.
