Ex-Bohs player Stephen O'Donnell proved to be the hero for the away side when he dispatched a penalty in the 95th minute after Ken Oman had fouled Karl Sheppard in the box.
It appeared Sheppard hadn't read the script for this game when he sent The Tribesmen into a shock, but deserved lead in the 16th minute with an excellent goal.
The goal came after a misplaced pass from Paul Keegan broke to 19-year-
old Sheppard, who coolly slotted the ball home past Barry Murphy.
Galway's joy proved to be short lived though, as Bohs equalised just seven minutes later. Keegan picked out Raf Cretaro at the back post with a delightful cross and the striker made no mistake, rifling the ball passed Barry Ryan.
Bohs, who had a devastating defeat at the hands of bitter rivals Shamrock Rovers in their last league game, got more into the game after they scored with Cretaro and Gareth McGlynn both looking menacing.
Galway were unsure if they would even have a fit and able goalkeeper going into the game, but Barry Ryan was passed fit to play and had an excellent game in the Galway goal and played a major part in their win.
There was a slight delay at half-time due to an injury to assistant referee Martin Maloney, but this didn't affect the visitors as they took the lead just five minutes into the second half.
Sheppard was constantly causing the Bohs defence problems and looked to be living up to his reputation as being a promising young player. It was he who again gave The Tribesmen the lead in the 50th minute as James Creaney's free-kick from the left-wing was powerfully headed past the helpless Murphy in the Bohs goal.
Bohs drew level again in the 76th minute when Ruaidhri Higgins' cross field pass found Conor Powell on the left-wing. He crossed the ball for Jason Byrne who scored with a simple finish.
Pat Fenlon made several changes to the Bohs team that faced Rovers last week but they didn't appear to work as The Gypsies lacked the bite and creativity to really dominate the game from start to finish.
Galway scored the winner in the 95th minute after Ken Oman brought down Sheppard inside the box. Oman was shown a second yellow card and O'Donnell comfortably scored the penalty to claim all three points.
The game ended on a sour note with two more red cards being shown. The first for a straight red for Cretaro for a needless kick-out at Sheppard and the second straight red card was for O'Donnell for his reaction.
The defeat makes it two league defeats from two for The Gypsies who now face a tricky Setanta Sports Cup second leg game away to Linfield on Monday.
Bohemians: Murphy; Heary, Powell, Cronin (Higgins '58), Shelly, Oman; McGlynn, Keegan, Cretaro; Madden (Quigley '73), Byrne.
Unused substitutes: Greene; McGuinness, O'Connor.
Galway United: Ryan; Conneely, Creaney, Foley, Sinnott; Ryan (King '83), O'Donnell, Meynell, O'Brien (McBrien '88); Sheppard, Flood.
Unused substitutes: Keane, Seoige, Keady.
Referee: D. Hancock
Extratime.ie Man of the Match: Karl Sheppard