A first-half header from Joleon Lescott gave Everton a deserved lead, but an impressive second-half performance saw the Reds draw level to take the tie to a replay at Goodison Park.
Liverpool started the brighter with a Xabi Alonso long-range drive within 30 seconds of the start, but a relieved Tim Howard in the Everton goal watched as the ball bounced well wide.
A frantic five minutes saw Fernando Torres cross for Ryan Babel only for Tony Hibbert to get across his man and at the other end, the Blues had a penalty shout after Steven Pienaar took a tumble in the box but replays showed a spot-kick would have been very generous.
The home side were spreading the ball well and forcing Everton to defend very deep and after good work from Steven Gerrard down the left, Jamie Carragher received the ball from his skipper inside the box and a moment of magic saw the defender skip past his man but his effort hit the side-netting.
With no Mikel Arteta in the side due to a cracked rib, Everton struggled to hold onto the ball and string more than a few passes together, but against the run of play David Moyes' men took the lead through a Lescott header.
After being instructed moments earlier to switch wings, Victor Anichebe chased down a long clearance and had no option but to drill the ball against Martin Skrtel and out for a corner.
But his hard work paid off as Pienaar whipped the dead ball on to Tim Cahill's head and Lescott was on hand to nod home from underneath the bar.
The game quickly returned to the Reds being allowed to spray the ball about the park and cross after shot was blocked and cleared by the solid pairing of Lescott and Phil Jagielka, who almost single handedly halted the waves of Liverpool attacks.
Even after the half-time whistle had the gone, things got worse for Liverpool as Carragher confronted referee Steve Bennett in the tunnel about time wasting from Blues keeper Tim Howard and after giving him several chances to walk away, Bennett was left with no alternative but to show the defender a yellow card for dissent.
It didn't take long from the restart for Rafa Benitez's men to be back on level terms after a moment of brilliance from Fernando Torres after 55 minutes when the Spaniard juggled to keep control of the ball before back heeling through to Gerrard, who smashed home the equaliser inside Howard's near post for his second derby goal in a week.
The Kop captain could have doubled his tally moments later when a Dirk Kuyt cross found Torres at the back post.
He chested the ball to Gerrard's feet but his first-time strike was superbly tipped over from close range by Howard.
Liverpool had to great chances to take the lead after a swift counter-attack saw the Reds three on two, but Gerrard's ball to Kuyt instead of Torres allowed Howard get his angles right and smother the shot on his first attempt.
The ball somehow managed to avoid crossing the line a minute later after good link-up play once again between Gerrard and Torres saw the striker swing his left boot from six yards but the ball bounced into the floor and wide.
Everton battled to hang on in the closing minutes and great defending ensured the 22nd FA Cup meeting between the two sides will go to a replay.