A single goal put away shortly after the first half hour by Gary McCabe proved the difference between the teams.
Galway huffed and puffed, won most of the aerial battles and intercepted any Bray passes that were less than perfect, but they failed to make use of their possession.
And even with a man advantage for the final half-hour, the Tribesmen were unable to break through a stubborn home defence.
Ronan Murray skied a first minute opportunity, and in the third, Conor Winn had a first taste of what would be a busy evening for him, diving at the feet of Dylan Connolly and McCabe who were disputing the attack.
Connolly then won a free which cost David Cawley a barely deserved caution, and from the set-piece the winger had a go, Winn parrying and Aaron Greene forcing a corner that came to nothing.
Galway showed good penetration on the counter-attack, Bray captain Conor Kenna pressed to clear at the cost of a throw.
When Connolly was brought down in a sandwich by Lee Grace and Stephen Folan in the penalty area, McLoughlin waved play on.
Shortly after the quarter-hour, Peter Cherrie was busy kicking a high bouncing ball clear from the edge of the area, and claiming well when Paul Sinnott's shot took a slight deflection on its way towards the goal.
Then Jesse Devers got behind the defence and nodded the ball ahead for himself, but a fraction too far and the Bray keeper was able to get to it first.
The home side was seeing more of the ball in the nextperiod, though when Colm Horgan brought McCabe down in the area, there was again no interest among the officials.
Mark Salmon struck a strong effort narrowly right of the target after good work in the left-hand corner just on the half hour mark, but then Kenna found his name going in the referee's book for a challenge in midfield, Marc Ludden's deadball landing in Cherrie's arms.
Minutes later, McCabe burst through the midfield, though a bounce on the feed by Greene seemed to take the ball to his arm en route, and shot. Winn got a finger to it, but only enough to turn it back into McCabe's path, and the Bray man made no mistake at the second time of asking.
The most the visitors had by was of a response before the break came from corners, the first conceded by Tim Clancy though Cherrie was arriving, and the second a simple catch for the keeper.
In between times, Hugh Douglas seemed to hold Conor Melody back by the jersey, but if he did it cost him as he needed attention after an awkward fall and was substituted before the whistle.
The Tribesmen put Bray under pressure in the opening passages of the second half, and the home side seemed out of sorts, relying on the back-pass even from midfield at times.
But it wasn't long before they recovered their composure, though they failed to make use of a brace of corners.
Salmon, who had shot over following the second of those, made an important contribution when he slid to dispossess Devers at the cost of a corner.
Greene and Connolly were combining well in a counter-attack when the latter slipped, allowing Winn to parry and Horgan to clear.
Just after the hour, another Kenna challenge caught the eye of the Referee, and a somewhat harsh if not debatable card resulted in the Bray skipper getting an early shower.
The stunned home defence managed to scramble Folan's free away, and after substitution a reorganisation followed.
With less than twenty minutes left, McCabe shot over from a Keith Buckley cross when it seemed easier to score.
A further dubious caution, this time for Lee Grace, added to a string of arguable offside flags, had both teams frustrated, and their irritation flared into a bout of handbags with ten minutes left, which it took all of McLoughlin's diplomacy to calm.
Just before that, Cherrie had dived well at the feet of Devers, and when ball resumed the same player shot left of the target when Horgan's crossfield feed reached him behind the left-hand post, and within minutes Devers, again in possession, had found only the top of the net from a narrow angle.
Bray manager Harry Kenny then withdrew McCabe, most likely for his own protection, as the winger's frustration threatened to boil over.
In four minutes of time added, Galway laid siege to the Bray goal, but to little effect, despite Cherrie having to concede a last-ditch corner.
It wasn't perhaps the prettiest football, but three points in the bag brought the Seagulls up to third in the table, a position they have rarely occupied beyond the first two or three matches of the season.
Bray Wanderers: 1 Peter Cherrie; 2 Hugh Douglas, 4 Conor Kenna (c) +=, 21 Tim Clancy, 15 Alan Kehoe; 3 John Sullivan, 8 Mark Salmon; 6 Keith Buckley, 11 Gary McCabe , 16 Dylan Connolly; 9 Aaron Greene