In a game which could have gone either way, the ‘keeper denied Curtis Jones and Conor Masterson from 12 yards to send City through after the young Blues had fought back in normal time to take the game to penalties.
Curtis Jones' close-range finish deservedly put Liverpool ahead after a period of dominance but the hosts were level before the break as Lukas Nmecha's free-kick deflected past Kamil Grabara to restore parity.
Both sides had chances to win the game, with the Reds taking control of the early proceedings, but Simon Davies' side improved after the break and carved a number of decent chances and remained calm to claim a 3-2 shoot-out win.
Faced with a Liverpool side who came flying out of the blocks, the Blues struggled to gain a foothold in the game in the opening 20 minutes.
Much like the first team encounter in January, the visitors were determined to disrupt City's passing game as early as possible and pressed all over the pitch, with the lively front three of Bobby Adekanye, Liam Millar and Ben Woodburn central to this.
Millar proved particularly threatening early on, tormenting Eric Garcia with his desire to get to the dead-ball line, but for all the Reds' possession, they failed to create any real chances.
A tame effort from Rafael Camacho was as troublesome as it got for Grimshaw and after a slow start, Davies' side rallied.
Ian Poveda was the beneficiary of one period of sustained possession as he cut inside from the right wing and fired just wide of Grabara’s left post from 18-yards.
The threat of Liverpool’s pacey attacking trident continued, and shortly after Garcia had prevented Adekanye from profiting on one counter-attack, Jones did just that.
Breaking up a City attack, the midfielder set Millar free down the right and the winger’s low centre deflected kindly into the path of the onrushing Jones, who fired home from six yards.
But City were level five minutes later - and in somewhat fortuitous circumstances.
The Nmecha brothers had combined with Lukas drawing a foul on the edge of the area and the skipper dusted himself down to see his deflected free-kick wrong-foot Grabara for a crucial equaliser on the stroke of half-time.
That goal and the chance to regroup saw City come out much improved in the second period.
Luke Bolton was particularly impressive, firing an effort goalwards immediately after the restart and then he so nearly turned provider with a spell of fine wing play.
Lukas Nmecha sent one teasing centre wide of the goal and then it was younger brother Felix’s turn to almost profit from Bolton’s efforts.
His cut-back reached the advancing midfielder, who looked to have found the bottom left corner on the half-volley only for Grabara to tip it round the post.
It was proving to be a much more even affair, but Liverpool’s threat was in no way diminished, with Millar and Adekanye constantly looking to stretch the City defence.
It was the latter who seemed most likely to find the breakthrough and Grimshaw needed a strong hand to keep out his near post drive as the contest entered its final 20 minutes.
But in Rabbi Matondo, introduced for Tom Dele-Bashiru, the Blues carried a similar threat on the counter and after the Welsh junior collected a clearance, he raced past two defenders only to see his toe-poked effort denied by Grabara.
With neither side able to find a winner, City were forced to benefit from the drama of penalties to book a place in the last four and it was Grimshaw again who thrived under pressure.
The 'keeper saved twice and after both Nmechas and Tommy Doyle had scored, Herbie Kane hit the crossbar to send City through to the semi-finals.
How City lined up
Davies made three changes to the team that beat Inter Milan in the last 16, with Brahim Diaz and Phil Foden away with the first team and Matondo dropping to the bench.
Bolton, Felix Nmecha and Iker Pozo came in to replace them.
Grimshaw was in goal and protected by a back three of Garcia, Joel Latibeaudiere and Ed Francis.
Matt Smith and Pozo anchored midfield with Dele-Bashiru and Felix Nmecha ahead of them.
Poveda and Bolton provided width either side of Lukas Nmecha up front.
What it means
We have reached the semi-finals of the UEFA Youth League for the first time in our history, where we will face Barcelona.
The semi-final takes place on Friday 20 April at the Colovray Stadium in Nyon, Switzerland.
Should City win, the final will be played three days later in the same stadium.