In a feisty contest at Leigh Sports Village, City took a deserved early lead through a stunning Vicky Losada strike.
But United levelled on the half-hour, despite protests that City keeper Karima Taieb had been fouled.
And the Reds clinched victory in the dying minutes, though City can still progress to the knockout stages of the competition.
What happened?
City looked like they had a point to prove after the weekend loss to Chelsea, tearing into United from the word go.
With an aggressive press unsettling the hosts, the Blues were ahead inside two minutes as Vicky Losada unleashed a thunderous rising shot from 20 yards that arrowed into the top left corner giving keeper Sophie Baggaley no chance.
Indeed, it was one way traffic for the first 20 minutes as City looked to capitalise on some nervy United defending.
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When the hosts did venture forward, they were met with committed defending from skipper Alex Greenwood and Ruby Mace, plus the high energy on either flank of Georgia Stanway and Demi Stokes.
But on the half-hour, the Reds drew level when Karima Taieb appeared the ball kicked out of her hands on the ground and eventually Ivana Ferreira Fuso was teed up and she thumped home from eight yards.
The City players protested long and loudly that Taieb had been impeded but the referee wasn’t interested.
It was harsh on Gareth Taylor’s side, to say the least and it with their tails up, United grew in confidence in the closing minutes of the first half.
Ellen White came on for the start of the second half, replacing Hayley Raso and just past the hour Lauren Hemp and Caroline Weir replaced Keira Walsh and Janine Beckie.
United almost cashed in on a loose pass on the edge of the City box, but Greenwood made a superb last-ditch tackle to save what looked a certain goal.
But the chances at either end were few and far between as the second period proved to be a much tighter contest.
But just as the game looked to be heading for a draw and a penalty shoot-out bonus point, United grabbed a second as Ona Batlle scored from the corner of the six-yard box after a superb Taieb save fell kindly for her.
How we lined up:
City: Taieb, Stanway, Mace, Greenwood (c), Stokes, Walsh (Weir 63), Losada (Angeldahl 78), Coombs, Raso (White 46), Beckie (Hemp 63), Park.
Subs: Pilling, Scott, Shaw
United: Baggaley, Thorisdottir, Mannion (c), Boe Risa, Thomas (Russo 53), Ferreira Fuso, Batille, Hanson, Smith (Blundell 79), Jones (Zelem 79), Staniforth
Subs: Earps, Blundell, Toone, Galton
What it means...
City have six points from three group matches in the Conti Cup and still top the table.
Only the group winners are guaranteed a knock-out spot, though a best runners-up place might still be enough for whoever finishes second.
Up next
City host Aston Villa at the Academy Stadium on Saturday morning, with a 11.30am (GMT) kick-off.
Victory will lift City above the sixth-placed Midlands side.
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