The Blues had all but sealed victory within the first half-hour following a Janine Beckie brace and a Jess Park tap-in.
Beckie added two more after the break with a Georgia Stanway penalty sandwiched in-between.
City were ahead after just 12 minutes against the Blades.
Esme Morgan’s low cross ended at the feet of Janine Beckie who planted a low drive past the keeper to claim her first goal for the Blues.
Seven minutes later, that lead was doubled as the returning Pauline Bremer, playing her first game for more than a year, wriggled in behind the United defence only to see her shot saved and then turned home by Jess Park from close range.
The Blues were showing no mercy to a Sheffield United side missing a number of first teamers and in 29 minutes, the game was effectively over as Beckie latched on to a poor back pass and coolly slotted past Alex Brooks to score her second of the evening.
With Keira Walsh spraying 40 and 50-yard passes to feet from the back and Claire Emslie tormenting the Blades down the left, it seemed like just a matter of when City would add to their tally.
Steph Houghton saw a header cleared off the line on 35 minutes from a corner, but the visitors dug in and could have pulled one back when a defensive mix-up allowed Sophie Jones a clear run at goal, but she powered a shot wide of Karen Bardsley’s left-hand post.
The rout continued after the break as Beckie completed her hat-trick just three minutes after the restart with a neat finish from eight yards out and four minutes later, Georgia Stanway was felled in the box and duly converted the Blues’ fifth of the night.
Beckie might have had another couple of goals but for a good save from Brooks and a shot that flashed wide.
But this was her night and on 78 minutes she scored her fourth of the evening following a superb mazy run by Lauren Hemp who jinked past two challenges before teeing up her team-mate to finish from close range.
City peppered the Sheffield goal in the time that remained but declared at six.
Star player: Janine Beckie
What it means…
The Blues are through to the next round of the Continental Cup with a game to spare.
City are yet to play Aston Villa but cannot be caught and top the group with 11 points.
City return to FA Women’s Super League action this Sunday, hosting third-placed Birmingham City Women at the Academy Stadium (kick-off 12.15pm).
Then it’s more Continental Cup action with the final group game away to Aston Villa Ladies on Thursday 13 December (kick-off 7.30pm)