Bournemouth started well and restricted their visitors in the first half, but four clear chances resulted in four goals to give the visitors to Totton command at the break.
Bunny Shaw gave City the lead shortly before the 20-minute mark, before three goals in the final six minutes of the first period left the Cherries reeling.
Lauren Hemp scored the second with a tidy finish, before two from Laura Coombs saw the sides enter the interval at 4-0.
Sophie Quirk _(Image: Richard Crease)_
Substitute Vivianne Miedema made sure of City’s progression with a second half brace, to see the Cherries’ unbeaten run in all competitions this season come to an end and to knock them out of the cup.
It was a strong Manchester City side led by former teammate of Cherries boss Helen Bleazard in Coombs, while WSL top goal scorer Shaw led the line.
Bleazard’s side to counter the Citizens was spearheaded by Bournemouth’s prolific duo of Sophie Quirk and Jenna Markham and skippered by Phoebe Williams.
The game quickly settled into a pattern, as City saw much of the ball early on, as anticipated by Bleazard and the Cherries.
But they limited the early chances for their WSL visitors, with a header off target the only half chance for the top flight side in the opening ten minutes.
The best early chance went the way of Bournemouth, as Katie James played a ball over the top for Markham, but her shot on the angle was saved well by Khiara Keating.
Bunny Shaw gave City the lead _(Image: Richard Crease)_
City made their possession count, though, and hit the front with 18 minutes on the clock.
Leila Ouahabi delivered a cross from the left and the prolific Shaw rose to guide her header past Erin Foley at the near post.
Yui Hasegawa dragged a shot wide from just outside the box not long after the opener, but the Cherries responded well to going behind.
But City were able repel the Bournemouth attacks and remained in control of the tie.
Hemp shot well over the bar from the edge of the D, before three goals in the final six minutes of the half gave City breathing space over their tier three hosts.
Jenna Markham _(Image: Richard Crease)_
With 39 minutes on the clock, Shaw turned and shot, it was blocked but Hemp followed up and finished well into the bottom corner from the left.
The pick of the first half goals was the third.
The ball was played into the feet of Shaw on the edge of the box, she turned and slipped a good ball in behind for Coombs, who fired past Foley for a very well worked goal.
Coombs completed her brace as she turned home a cross from the left from Shaw, to give City firm control at the break.
Foley caught comfortably from a Shaw header in the opening minutes of the second period, before the striker pivoted and shot just wide not long afterwards.
Three goals in the final six minutes of the first half gave City control. _(Image: Richard Crease)_
A good double save from the Cherries keeper first denied Ouhabi from range and then Shaw moments later.
Hasegawa rattled the crossbar with a thunderous effort ten minutes into the second period.
City had their fifth not long after, as substitute Miedema tapped home from close range after a Foley save and a block saw the ball go back across goal to the Dutch striker at the back post.
Bleazard introduced Amber Treweek, Molly Barron-Clark and Elena Cole for Meadows Tuson, James and Wilson shortly after the hour mark.
Kenni Thompson _(Image: Richard Crease)_
Harris headed off the line from a Miedema header, before Foley denied the forward brilliantly when one-on-one.
Quirk and Markham were replaced by Gemma McGuinness and Zoe Barratt with just under 15 minutes to play.
Laura Blindkilde Brown shot over the bar on the angle, before a sixth City goal saw Miedema complete her brace with six minutes to play.
She found some space to shoot and rifled the ball into the bottom corner with a powerful effort that left Foley no chance.
The Cherries keeper smothered a Miedema shot as the game entered stoppage time, during which Ouahabi was denied the City seventh by the offside flag.
Treweek volleyed over a good chance after a free kick from deep was punched out to her by Keating in what was the final chance of the game, as the Cherries were well beaten by their WSL visitors.