Having dominated the first half, the hosts had started to build more pressure against the wind in the second only for Salmon to strike on the break, sprinting inside Georgia Brougham before finishing one-on-one past Hannah Hampton.
Manager Marta Tejedor made five changes to the team that won 1-0 at Sunderland in the Women’s FA Cup.
Hampton, Brougham, Adrienne Jordan, Lucy Whipp and Abbi Grant came in with Alex Brooks, Rebecca Holloway, the suspended Lucy Staniforth, Connie Scofield and Claudia Walker making way.
Blues began brightly and subjected the visitors to a couple of close shaves early on, Rachel Williams seeing her connection on a low free-kick from the right ricochet to safety.
Williams then held up from a throw-in, laying off for Brianna Visalli to drive at the near post with Sophie Baggaley forced to parry wide.
The pressure kept coming with Sarah Mayling’s inswinging corner swatted out of a busy six-yard box by Baggaley and Jordan’s bending ball to the back stick a little too high for Mayling steaming in.
Williams held up for Grant to release Visalli with her first touch but the American was put under pressure with her low shot smothered by Baggaley.
The Robins produced a well-crafted opening in the 31st minute, Katie Robinson working her way back inside on the right to cut back for Charlie Wellings but the cross was behind her, making it easy for Hampton to gather the shot on the spin.
Williams again surged forward and on to Grant’s touch into the box but neither the experienced striker nor Visalli could get a telling connection before Baggaley slid out to gather.
More well-worked play saw captain Kerys Harrop stride forward and take a swing from 20 yards which bounced narrowly wide, while Williams had a shot dip narrowly over the crossbar from 18 yards after Grant’s initial effort had been charged down three minutes before the break.
With the wind at the their backs, the Robins got farther up the pitch early in the second half and a speculative shot from Yana Daniels hit the top of the crossbar on its way over, one that Hampton seemingly had covered.
Walker fired a shot to the near post shortly after coming on as Blues steadily rebuilt momentum and later pinched possession from a loose ball in the box but the route to goal got slammed shut on Grant.
The sting in the tail arrived 14 minutes from time when Salmon dashed on to a lofted ball forward and got in behind Brougham to finish despite the exposed Hampton getting a touch.
Blues kept plugging away but belief was punctured by conceding and Olivia Chance’s wind-assisted dig from distance had to be pushed against the bar by Hampton with five minutes to go.
Jordan’s cross and Mayling’s corner were both cut out as Blues forced back their rivals during added time, while Walker’s centre was a little too high for the leap of Harrop at the death.
Blues: Hampton, Jordan, Harrop, Brougham, Scott (Walker 59), Visalli (Scofield 79), Whipp, Kelly, Grant, Mayling, Williams.
Unused subs: Holloway, Brooks (g/k).
Bristol City: Baggaley, Pattinson, Matthews, Brown, Bryson, Chance (Allen 87), Logarzo, Daniels, Jeon (Wynne h-t), Wellings, Robinson (Salmon 65).
Unused subs: Jones, Collis, Sanford, Cumings (g/k).
Goals: Salmon 76.
Referee: Stacey Pearson.