Ben Hinchcliffe’s first-half strike from a rebound ensured Hull took a 1-0 lead into the break, but Liverpool responded thanks to Matty Virtue’s close-range equaliser.
Despite the best efforts of both sides, neither could find a winner in normal time, with extra-time needed to separate them.
Toni Gomes’ expert finish from Ojo’s cross looked to have sealed a quarter-final berth for the Reds youngsters, only for Luke Lofts to coolly make it 2-2.
The agony of a penalty shootout was left to decide who would progress, and fortunately, it was Liverpool who held their nerve.
Kevin Stewart, Gomez, Madger Gomes, Nathaniel Phillips and Gomes all converted their spot-kicks, although Ojo fired his effort over the crossbar.
It didn’t matter, though, as Will Annan and Brad Maslen-Jones missed for the hosts, confirming Liverpool’s place in the quarters.
Some of Hull’s players were full of praise for their opponents post-match:
Devastated to get beat on penalties after a game like that against Liverpool. Lads were unreal n done ourselves proud ??
— brandon (@brandonflemingg) March 19, 2017
Gutted to lose on penalties against Liverpool, lads were unreal?very happy to finally get back out there after a long 3 months??
— tyler hamilton (@hamilton_99) March 19, 2017
Gutted to lose on penalties against Liverpool lads were different class?? we go again Thursday???
— Ben Hinchliffe (@benhinchliffe) March 19, 2017
Speaking after the game, Garrity spoke of his pleasure at the result, as well as the importance of more game time for Gomez and Grujic.
“We are pleased to qualify for the next stage of the competition because this was a tough game,” Garrity told Liverpoolfc.com.
“Hull City worked hard and made it tough for us at times but the lads battled well.
“It was good to see Joe [Gomez] last the full distance and Marko [Grujic] get more minutes and both lads are getting stronger.”
Liverpool: Kelleher; Whelan, Phillips, Gomez, Randall; Stewart, Virtue, Grujic (Alves 106′) Ojo, Dhanda (M. Gomes 67′), T. Gomes
Subs not used: Williams, Brewitt, Juanma