Luis Suarez opened the scoring on 23 minutes with a classy finish, only for Peter Crouch to level four minutes later with a header against his former club.
Stewart Downing then struck with only his second Liverpool goal in the second half to send the Reds back to the national stadium, where they won the Carling Cup final last month.
Typically for a game involving Stoke, it was a highly combustible affair, with referee Kevin Friend showing four yellow cards in the first half. However, the Potters backed themselves to play football against the Reds, and often played the ball around on the deck every bit as well as their hosts.
Maxi Rodriguez had a good chance to open the scoring in only the second minute, flying in to meet Steven Gerrard's cross with a header that went just over the bar.
Suarez was at his most impetuous, with all the gestures, theatrics and waving of imaginary cards we have come to expect from him, but the Uruguayan gave another reminder of his immense talent midway through the first half.
After playing a one-two with Maxi, Suarez passed a well-taken low finish past Thomas Sorensen that hit the bottom corner. It was Suarez's 11th goal of the season, and his first since Liverpool beat Brighton 6-1 in the last round of the competition a month ago.
Stoke were only behind for four minutes, but their equaliser came in controversial circumstances. Ryan Shawcross got the only touch on a Stoke corner which went out of play on the other side of the pitch, but the officials awarded another corner. From the subsequent set piece, Ryan Shotton stood right in front of Pepe Reina, and the impeded goalkeeper was powerless to stop former Liverpool striker Crouch heading home from the corner.
Jonathan Walters fired wide of the near post after being released by Dean Whitehead before Gerrard struck a free-kick over the bar, but the sides were level going into the break as fans around the ground chanted the name of Bolton midfielder Fabrice Muamba, who remains in a critical condition in hospital after suffering a cardiac arrest during Saturday's tie at Tottenham.
Suarez came agonisingly close to scoring his and Liverpool's second early in the second half when Downing whipped in a superb curling free-kick from the left, but the forward's glancing header went wide of the far post.
Having almost set up Suarez to put Liverpool ahead once more, Downing then ended up doing so himself on 57 minutes. The England winger's short pass to Gerrard on the edge of the box rebounded off the captain's heel, and he reacted quickest to pounce on the loose ball, surge into the box and blast a finish close to Sorensen but too quick for the Dane to react.
The goal was downing's first for Liverpool against top-flight opposition, having opened his account against Oldham in the third round of this competition.
Both managers made changes soon afterwards, with Tony Pulis bringing on another ex-Liverpool player, Jermaine Pennant, while Kenny Dalglish introduced Dirk Kuyt.
As clear chances started coming increasingly at a premium, Suarez hit a fizzing strike from range but Sorensen was equal to it.
Pulis brought on Cameron Jerome and Rory Delap for the final 20 minutes, whilst Suarez and Martin Kelly were taken off in the final minutes both nursing injuries, but none of the changes could affect the scoreline and keep Stoke's hopes of a second FA Cup semi-final in two years alive.