Izzy Christiansen and Georgia Stanway put the Blues into a two-goal lead before goals from Toni Duggan and Jane Ross sealed progression into the last four after Marta Mathews had reduced the deficit.
Nick Cushing made four changes to the side that beat Reading in midweek with Marie Hourihan, Keira Walsh, Daphne Corboz and Duggan coming in for Karen Bardsley, Jill Scott, Ross and Stanway.
City were on the front foot from the off and created a half chance in the opening minute but Nicola Hobbs was out quickly to smother the danger at the feet of Nikita Parris.
The pressure continued and Parris was involved in the action in the 10th minute as she intercepted a back pass and fired narrowly wide from a tight angle.
Doncaster rarely tested Hourihan in the first half with Christie Murray coming the closest when she saw her long range shot drift over the crossbar.
From the resulting phase of play, Cushing’s side thought they had opened the scoring when Christiansen tapped in Corboz’s low cross but the goal was chalked off with the former being ruled offside.
Chances for the Blues continued to flow as the first half reached its midway point with Duggan seeing a shot fly past the outside of the post before Hobbs pulled off an impressive save to deny the 25-year old.
The waves of attack were relentless and the pressure paid off in the 38th minute when City took the lead through Christiansen.
Demi Stokes sent in a cross towards the penalty area from the byline and City’s number 11 rose above her marker to float a header over Hobbs and into the back of the net for 1-0.
Three minutes of added time were indicated at the end of the first half and Cushing’s side created one final chance before the whistle sounded.
Duggan found herself in space on the left hand side of the area and sent a shot towards the top corner, only to see it go inches wide of the post.
Cushing’s side continued to dominate after the restart and came close to doubling their lead on two occasions.
First, Steph Houghton’s low free kick was saved by Hobbs before Lucy Bronze was inches away from converting Duggan’s corner at the back post.
Following the flurry of chances, the game calmed down before sparking into life with three late goals.
Substitute Stanway continued her fine form as she added City’s second with a wonderful strike from 25 yards out that nestled into the bottom corner past the dive of Hobbs.
At the other end, Hourihan was tested for the first time when she tipped Kasia Lipka’s effort around the post but she couldn’t do anything to prevent Marta Mathews reducing the deficit shortly after.
However, it only took two minutes for the Blues to restore their two-goal lead when Duggan fired in from just inside the area to all but seal the result.
Progression into the semi-final of the Continental Tyres Cup was confirmed in the 88th minute through Ross, when she slotted home from close range from Stanway’s knockdown to seal the victory.
