Right-back Kelly did his first-team ambitions no harm with a goal early in the second half at Prenton Park only to have it cancelled out within minutes by Jordan Mustoe.
The result, which makes it 15 unbeaten for John McMahon's youngsters, leaves them six points behind league leaders Manchester United with three games in hand.
It took 16 minutes for either side to create a goalscoring opportunity, and it came when Wigan left-back Daniel Redmond sent in a wicked cross which Adam Buxton really should have converted.
Five minutes later Liverpool responded with a nicely floated free-kick to the far post from Francisco Duran. Daniel Ayala headed across goal for Lauri Dalla Valle but goalkeeper Lee Nicholls was sharply off his line to intercept.
McMahon's side were soon threatening again when a right-wing cross bounced to the head of Alex Kacaniklic, who attempted to nod the ball over Nicholls only to be denied by a superb fingertip save.
Rachid Bouaouzan drove towards the Liverpool area before unleashing a low drive too close to Martin Hansen with 15 minutes of the half remaining, while at the other end Jordy Brouwer dragged wide from 30 yards.
The final chances of the first period fell to Dalla Valle, first at the far post after some slapdash defending from Wigan, who were again saved by their goalkeeper. Next the excellent Duran swung in another perfect cross which the Finn headed against the crossbar.
The Wirral rain had started teeming by the time the teams emerged for the second half, but it didn't deter Damien Plessis from surging down the right to send a tantalising cross towards Brouwer, who mis-kicked from six yards.
Minutes later Steven Irwin volleyed too close to Nicholls after Kacaniklic's cross but it was Liverpool who were now firmly on top.
The opener was deserved, then, when it arrived 12 minutes into the half through Kelly, who was there to blast home when Brouwer knocked Duran's free-kick back across the six-yard box.
Wigan didn't let their heads drop, however, and two minutes later were level when Mustoe drilled into the bottom corner from a 20-yard dead ball.
Liverpool almost restored their lead when centre-back Victor Palsson steamed forward to centre for Dalla Valla, who failed to connect properly with a diving header.
Irwin then came close with a speculative effort, while substitute Nikola Saric glanced wide from eight yards.
Goalscorer Mustoe might have had his second when another set piece hit the wall before looping narrowly over the bar.
Wigan ended the game with 10 men after Steven Boothman was dismissed in injury-time for a professional foul on Brouwer.
Seconds later Dalla Valle had a golden opportunity to capitalise and seal the three points but was smothered out of it by the goalkeeper after a sublime first touch.
Liverpoolfc.tv man of the match: Francisco Duran.
Hansen, Kelly (Flanagan 71), Mavinga, Ayala, Palsson, Duran (Cooper 60), Dalla Valle, Irwin, Brouwer, Plessis (Saric 68) , Kacaniklic. Subs not used: Oldfield, Kohlert.