Khadija Shaw opened the scoring for City midway through the first half but the Reds soon drew level courtesy of Katie Stengel at the Academy Stadium.
The home team went on to claim all three points 15 minutes from time, however, as Hayley Raso pounced to convert at the second attempt.
Liverpool’s preparations were hindered during the warm-up as Ceri Holland had to drop out of the original starting XI, with Rachel Furness brought in by Matt Beard.
And the visitors had to ward off sustained early pressure from City during the opening stages, with Lauren Hemp twice threatening from successive left-wing corners.
She first flicked a low effort narrowly wide of the near post via a deflection or two, and then followed up with another harmlessly over.
A dangerous cross from open play created City’s next opportunity, Deyna Castellanos swinging it into the area for Shaw, whose downward header was well fielded by Rachael Laws.
But the home side broke through with 21 minutes on the clock.
Hemp was the creator with a deft dribble at the edge of the Liverpool area and a pass slipped in to Shaw on the left, and the striker this time made no mistake by sweeping a shot beyond Laws.
The Reds responded well, though, steadily gaining a foothold in the encounter and increasingly troubling the opposition with a high-pressing strategy.
It could have yielded an equaliser in the 32nd minute, when Missy Bo Kearns cut out a pass from the goalkeeper at the edge of the City box but sent her return strike too close to Ellie Roebuck.
But the tactic bore fruit seconds later.
Stengel stole the ball from Alex Greenwood around 20 yards from goal, moved forward and tucked an excellent finish past Roebuck to bring Liverpool level.
The American might have put her side in front before the break, too. However, having been found in space by Kearns’ corner delivery, she connected with more shoulder than head and sent the ball off target.
The pattern of play continued in a similar vein after half-time, with City mounting plenty of pressure but with Liverpool a clear threat whenever they attacked.
Chloe Kelly could do little more past the hour mark as she made space down the right channel and fired a cross into Reds territory that no teammate could connect with.
The visitors then had to produce two massive interventions to deny City another lead.
Niamh Fahey brilliantly blocked a central drive from Yui Hasegawa and when the rebound was nodded over Laws and on course for goal by Hemp, Megan Campbell scurried back to clear away from the line.
But City produced the decisive moment with a quarter of an hour remaining.
Shaw echoed Hemp’s earlier dribble and threaded assist for substitute Raso, who found the roof of the net after her first shot was repelled by Laws.
The Liverpool goalkeeper had to make a stunning close-range stop to prevent Laura Coombs from putting the result beyond doubt a minute from the end, but City saw it out to take the victory.
LFC Women: Laws, Koivisto (Wardlaw, 90), Flaherty, Fahey, Campbell, Hinds (Roberts, 83), Matthews, Furness (Van de Sanden, 76), Kearns (Humphrey, 76), Lawley (Daniels, 76), Stengel.
Unused substitutes: Cumings, Robe, Silcock.