Stewart Downing produced the most telling contribution of his Liverpool career to fire the Anfield club past Stoke and into the FA Cup semi-finals.
Luis Suarez gave the hosts the lead with a curling 20-yard strike after a one-two with Maxi Rodriguez.
But Peter Crouch's header from a corner earned Stoke a deserved equaliser.
The Reds picked up the pace and were rewarded when Downing drilled a shot past Thomas Sorensen to book a Wembley date with either Everton or Sunderland.
Liverpool's victory fully justified Kenny Dalglish's pre-match assertion that the club are making progress under his stewardship despite an inconsistent Premier League campaign.
And the Reds are now two Wembley wins away from a cup double in the Scot's first full season since returning to the club where he enjoyed success after success as a player and manager between 1977 and 1991.
Stoke, runners-up last season, fully deserved to be level at half-time after a combative display full of energy and purpose, but after Downing's intervention they never really looked likely to fashion an equaliser.
Liverpool's early attacks lacked finesse, with several final balls going astray until Suarez decided to take matters into his own hands.
Running with the ball towards the heart of the Stoke defence, he exchanged passes with Maxi and curled a delightful shot into the bottom corner.
Stoke responded with a sustained offensive on the Liverpool goal that swiftly produced an equaliser as Crouch shrugged off the attentions of Andy Carroll and headed a Matthew Etherington corner past Pepe Reina.
The home goalkeeper was booked for protesting in the aftermath, with replays showing that a goal-kick, rather than a corner, should have been awarded.
With Liverpool's passing devoid of the fluency that marked the recent home displays against Arsenal and Everton, Stoke came closest to taking the lead before half-time.
Dean Whitehead's slide-rule pass put Jonathan Walters in behind the Reds defence on the right but his powerful shot flew well wide of the near post.
Liverpool began the second half on the front foot as Gerrard tested Sorensen from long range and a Suarez header from a Downing free-kick fizzed across goal.
Then came Downing's moment, as he burst into the box from the right flank and, after benefiting from a deflection off Gerrard's heel, smashed a left-footed shot back across Sorensen and into the net.
Despite the introduction of fresh legs, Stoke struggled to cope with wave after wave of Liverpool attacks.
Substitute Dirk Kuyt stung the palms of Sorensen from long-range before Jay Spearing blazed over the bar from a promising position.
Substitute Cameron Jerome wasted Stoke's best opening when he raced beyond the Liverpool defence but hesitated, allowing Martin Kelly time to get back and block his shot.
Rory Delap's long throws caused one or two nervy moments during six minutes of added-time but the Liverpool defence, marshalled by Jamie Carragher, held on.