After a cagey opening, Glasgow struck first on 15 minutes when a swift transition from defence saw Briar McNamara feed Sky Phimister, who showed her pace to go in from halfway.
Despite creating chances, the Warriors went into the break trailing 7-5 after being caught out by a quick Gwalia tap that led to a Tilly Vucaj try.
The hosts started the second half strongly, with a great run by Freya Walker putting her over early on but that momentum was short-lived as Gwalia responded almost immediately, Molly Reardon touching down to level the scores at 12-12.
Another see-saw swing followed when Gemma Bell powered through the Gwalia defence in the 55th minute to put Glasgow back in front, but errors again punished the hosts as Courtney Greenway turned the tide, scoring a late hat-trick to pull the visitors clear and seal the win.
Speaking after the match, Glasgow Warriors Head Coach Lindsey Smith said: "It was a bit of a frustrating match as we played well in parts, but we also didn't look after the ball well enough and we got punished for it.
"It's a learning experience for a lot of the players and they are still relatively young but overall there were some aspects that we were pretty pleased with today but we are still looking for that 80 minute performance.
"It was great to see the crowd turn out to Scotstoun today and see the players interacting with the kids on the pitch at the end too."