The Reds were good value for their win after creating numerous openings across the 90 minutes, but they were ultimately made to work hard for the victory which arrived 11 minutes from time at Prenton Park in the all-Merseyside affair.
Congestion around the ground prior to kickoff led to the match being delayed by 15 minutes, but the visitors were quick to get at their less illustrious opponents.
Kent came close to making a breakthrough just six minutes in with a well-hit shot that stung the palms of Scott Davies, before firing narrowly wide of the target moments later.
Jurgen Klopp's side were well in control as the half wore on, with Mane's biggest involvement seeing him play the ball through for Roberto Firmino to race in behind, only for a poor first touch to let the Brazilian down.
Liverpool made 11 changes at the break, including the introduction of eventual matchwinner Ings, who was given the role of captain for the second half.
Lazar Markovic somehow missed from six yards out when trying to convert a saved Ings shot, while the ex-Burnley striker was himself wayward with a couple of headed chances as Klopp's men continued to struggle in front of goal.
The breakthrough moment did finally arrive late on, though, as Alexander Arnold burst forward and fed the ball to Ings, who was able to smash it in via the post from 15 yards out.