United took the lead early on when Beth Lumsden found the top corner after some nice edge of the area play from Jordan Nobbs, but were pegged back on the stroke of half time by Rio Hardy.
Then, after the Lasses failed to clear a corner, Gale pounced on a bouncing ball in the six-yard box to score with one of the final touches of the game.
With the backing of a strong away contingent, United came flying out of the blocks to put in a solid performance for their fans and could have been ahead inside five minutes.
A long ball down the wing released Emily Murphy, who drove into the box before cutting the ball back to Nobbs, although the pass was slightly behind the number four, and her effort lacked conviction and fell into the arms of Lauren Brzykcy.
However, the Lasses maintained their high intensity and level of performance into the 19th minute when Lumsden scored her fifth league goal of the campaign.
A lofted Freya Gregory cross was only cleared to Nobbs on the edge of the area, and her calm first touch took Sophie Ingle out of the game and set up Lumsden to arrow her strike into the top corner.
A two-minute spell almost saw Newcastle add a second before the break. Firstly, Murphy received the ball on the half turn before seeing her outside of the box strike take a wicked deflection and dip over the bar.
From the resulting corner, Gregory played it short to Nobbs, who gave it back to the Scotland international. She aimed for the bottom corner but it rippled the side netting.
Despite the Lasses playing on the front foot and looking the more dangerous side, an Ella Powell long ball in behind Jemma Purfield saw Hardy bear down on goal before calmly finishing beyond Anna Tamminen from close range.
The blow of conceding just before half time didn't appear to knock Tanta Oxtoby's side as Lumsden was slipped through one-on-one with a perfectly weighted ball from Nobbs, but the number 26 could only lift her effort over both the keeper and the crossbar.
United were continuing to find joy through the connection of Nobbs and Lumsden, with the former releasing the winger away again to bear down on goal, although this time she was forced to shoot off balance due to the recovery run from Gemma Lawley, making it a simple save for Brzykcy.
It was all Newcastle in the second half, and they were millimetres away from retaking the lead after a hacked clearance from Bristol City saw the ball fall to Lumsden, who looked to have scored, but after a save from Brzykcy, the ball spun on the line, refusing to go over.
The Robins almost hit United with another sucker punch when they swiftly counter-attacked after a wasted Newcastle free-kick that ended up with Lexi-Lloyd Smith being played in one-on-one against an on-rushing Tamminen, but it was the Finn who came out on top with a brave low save.
Bristol City were becoming increasingly dangerous on the counter-attack as they worked a three-on-one situation with Lloyd Smith picking out Emily Syme in the six-yard box, but she was denied from close-range by Tamminen, before a last-ditch Jorja Fox tackle stopped Maria Farrugia from putting her side ahead on the rebound.
Ashton Gate was ready to celebrate an added-time winner for the home side with Lloyd Smith delivering a perfect cross to the back post for an unmarked Gale to head into an empty net, but from a couple of yards out, the on-loan Arsenal forward headed wide.
Substitute Gale was the hero for Bristol deep into stoppage time, though, with her close-range finish sending the home fans wild after United were unable to deal with a bouncing ball in the box.
Newcastle United Women: Anna Tamminen, Demi Stokes (c), Jordan Nobbs, Jemma Purfield (Jorja Fox 77), Morgan Gautrat, Emma Kelly (Lois Joel 77), Freya Gregory, Deanna Cooper, Aoife Mannion, Beth Lumsden (Oona Sevenius 88), Emily Murphy (Emilia Larsson 66)
Subs not used: Hannah Hawkins, Shania Hayles, Małgorzata Grec, Ashanti Akpan
