The first goal of Natasha Dowie’s second spell with the Reds had secured a 16th-minute advantage, but Lauren Hemp’s header soon brought City back on terms.
An excellent finish from Kearns put the hosts in front again two minutes into the second half, however, and that proved enough to take all three points in the Barclays Women’s Super League.
The visitors made a confident start to proceedings at Prenton Park and threatened to take the lead inside the first three minutes.
Faye Kirby misjudged her clearance outside the box and sent it straight to Laura Coombs in sky blue. She immediately tried to loft a shot back over the Liverpool goalkeeper, who recovered well to tip the ball up into the stands.
City had settled into an attacking pattern but it was the home side who opened the scoring just seconds past the quarter-hour mark.
As the opposition looked to play out from the back, Coombs directed a pass to Dowie rather than her ’keeper and the Reds striker dispatched a low, reverse finish past Ellie Roebuck and inside the left post.
City levelled around 10 minutes later, however. Chloe Kelly worked space on the right byline and hoisted a cross to the back post, where Hemp arced a looping header into the opposite corner of goal.
The same combination then almost worked again as Kelly burst through in the left channel and unselfishly squared the ball across the area for Hemp, whose drive was blocked by Jasmine Matthews.
The Reds rallied as the interval approached, though in added time Khadija Shaw broke in behind and a had a chance to shoot, only to drag her left-footer wide of Kirby’s net.
Liverpool retook the lead just two minutes after the restart and it was courtesy of a precise Kearns finish.
Ceri Holland’s raking pass from left to right had been glanced on by Kearns to Emma Koivisto and when she received the ball back inside the box, the No.7 swept it low beyond the reach of Roebuck and into the left corner.
Reds boss Matt Beard subsequently introduced Shanice van de Sanden from the bench and the forward had to be denied by the gloves of the City ’keeper having been released via Katie Stengel’s assist from deep.
Koivisto saw a cross from the right flank bounce away off the left post, Steph Houghton slid a strike from 20 yards narrowly off target at the other end, and then Roebuck rushed from her line to thwart Van de Sanden one-on-one.
City continually pressed for a way back into the match and a dipping effort from Hemp clattered the underside of the crossbar, bounced down and was cleared by Matthews, with the officials judging it had not gone over the line.
Esme Morgan skewed a decent close-range chance wide as nine minutes of stoppage time got under way, but the Reds resolutely saw it out to clinch a brilliant victory.
LFC Women: Kirby, Koivisto, Roberts, Matthews, Bonner, Hinds, Nagano, Kearns (Taylor, 77), Holland, Stengel (Lundgaard, 90+1), Dowie (Van de Sanden, 50).
Unused subs: Laws, Cumings, Robe, Fahey, Kiernan, Humphrey.