Brandtman broke Friday night's deadlock in the 57th minute, cutting back inside before unleashing a beautiful left-foot strike from outside the box to beat diving goalkeeper Matthew Sutton.
It was the 20-year-old's first goal in what was his 22nd ALM appearance and ninth start, with the moment silencing the 5889 crowd at HBF Park.
The Mariners now have two wins and a draw from four games under interim coach Warren Moon, who was thrust into the hot seat when title-winning mentor Mark Jackson left on the eve of the season.
"He's a good young player," Moon said of Brandtman.
"We spoke at halftime about just being a little bit more accountable and brave in those moments.
"We had some opportunities first half. We weren't quite brave enough to either take the strike or get into a good area and get crosses into good areas as well.
"So we spoke about that, and Bailey came up with a great moment for the match."
Glory, wooden spooners of the past two seasons, remain bottom of the ladder with just one draw to show from four matches.
Perth interim coach Adam Griffiths has now presided over two losses since David Zdrilic was sacked following the 4-0 loss to Melbourne City in round two.
The club's hierarchy could announce the appointment of a permanent coach as early as next week.
"We came out sluggish, naive in terms of our approach," Griffiths said of his team's sloppy start to the second half.
"Then they got the goal, and that moment changed the game really."
Glory dominated the first half, firing off four shots on target to Central Coast's none, as well as enjoying 55 per cent possession.
Son-of-a-gun Sebastian Despotovski, whose dad Bobby was a Glory goalscoring hero, had a great chance to open the scoring in the 19th minute, but couldn't get his lunging strike on target.
Mariners goalkeeper Andrew Redmayne came to the rescue in the 29th minute by tipping away Adam Taggart's long-range lob.
Taggart had a few good looks, but the Mariners' defence remained steadfast to ensure the scores remained locked at 0-0 at half time.
The Mariners upped the ante to start the second half, and some individual brilliance from Brandtman got the visitors on the board.
Glory got increasingly desperate as the match wore on, with Taggart looking dangerous at times, and substitute Khoa Ngo adding some much-needed spark.
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