Just when the Bulldogs' halves headache looked set to throb into next week, much-hyped mid-season recruit Galvin broke the Dragons' hearts with a cut-out ball to Jethro Rinakama in the final 90 seconds at Accor Stadium.
Dragons winger Tyrell Sloan was caught in-field and his opposite man Rinakama, in only his second game, slid over to seal a win that will help Galvin keep the No.7 jersey.
The move to bring Galvin over from Wests Tigers had been questioned as coach Cameron Ciraldo deliberated how best to use the 20-year-old in a team that had been atop the ladder when he arrived.
But the magic play hit back at the critics and stunned even the coach.
"It's possibly one of the bravest passes I've seen," Ciraldo said at fulltime on Saturday night.
"We all know he's had pressure on him. I can't rap him (enough) for how well he's handled it.
"To trust his instincts and trust himself to make that play just shows everyone what we've been seeing at training for the last six weeks.
"(I'm) really happy for him."
Ciraldo had made up his mind even before the game-winning play that he'd be giving Galvin an extended run at halfback after weeks of uncertainty as to whether he or Toby Sexton should see the season out in the crucial position.
"I've got to say, even before that last pass, I'd seen enough," Ciraldo said.
"Whether he makes that pass or not, there was a lot in his game that I liked tonight."
The loss leaves the Dragons' finals hopes hanging by a thread.
Saints are still a mathematical chance but need to claim victory in all of their remaining games to finish the season with a winning record, and face Penrith, Canberra and the Warriors on the run home.
Saturday night was the eighth time this season the Dragons have lost by 10 points or fewer.
Veteran recruit Clint Gutherson had thrown the last pass to Sione Finau that gave the 11th-placed Dragons an unlikely lead in a second half.
They looked home and hosed, stoically defending the Bulldogs on their goal-line in the final minutes having run in the first two tries of the second half.
But coach Shane Flanagan was frustrated the Bulldogs had even been in position to score the match-winner after a controversial captain's challenge call from the bunker.
On review from the Bulldogs, Dragons forward Luciano Leilua was ruled to have crowded Jacob Kiraz in the ruck, leaking a penalty that helped Canterbury move upfield and win the game.
"I was really proud of the effort they put in and the way they played, but the game was taken away from us from, I believe, wrong decisions," Flanagan said.
Earlier, Galvin backed his captain Stephen Crichton up on the right side to score his side's second try, and came close to putting Viliame Kikau over for four-pointers in each stanza.
But Damien Cook made a heroic effort to hold Kikau up over the line, before referee Adam Gee found a knock-on prior to Galvin's kick finding its way to the giant forward.
Finau dislocated his shoulder in the act of scoring the Dragons' third try, while Bulldogs recruit Sitili Tupouniua hurt his hamstring in his first game back from a lay-off with that same injury.