A second-half strike from Melissa Lawley was cancelled out by a fantastic Missy Goodwin effort before a late opening for Hobinger allowed the hosts to take the points as City were handed their second defeat of the 2023/24 Barclays Women's Super League season at Prenton Park.
There were two changes to the Leicester side beaten by Manchester City last time out in the league, with Shannon O'Brien and Aileen Whelan not included in the matchday squad and Goodwin and Josie Green coming into the fold.
It was the hosts who started strongest, pressing on loose balls from the City defence, but at times this created openings for the Foxes to exploit. When CJ Bott drove forward, she played a ball out to Hannah Cain before continuing her run into the box. The New Zealander couldn't connect with the low cross, however.
Ten minutes before the break, the Reds had their best opportunity when Sophie Roman Haug sent a looping effort towards goal, but a back-peddling Janina Leitzig managed to pull off an extraordinary save to tip it behind.
The last chance of the half fell in favour of the Foxes when good play down the left wing allowed Jutta Rantala the chance at goal, but the midfielder's left-footed shot, curling to the far post, was well saved by Rachael Laws.
The deadlock was eventually broken by the Reds who took the lead following the restart when Lawley managed to break through the Leicester defence, and sent a powerful effort into the roof of the net, past the helpless Leitzig who had made several saves prior to conceding.
City did get back level just before the hour mark through Goodwin, when the young winger made half a yard for herself against the opposing defender and fired a left-footed strike into the top corner from a tight angle.
After a couple of changes, which saw Deanne Rose and Janice Cayman introduced, Leicester pushed to take the lead, but it was Liverpool who produced the decisive moment. On the break, a low cross from the left wing found Hobinger, who turned it goalwards with five minutes of normal time to go.
There was no late response from City, who will be disappointed not to take any points this weekend. Willie Kirk's side will now turn their focus to Arsenal, who they welcome to King Power Stadium for a 6:45pm GMT kick-off on Sunday evening.