Gerrard struck nine minutes after halftime to cancel Joleon Lescott's first-half header as the game finished with the same score as their Premier League meeting on the same ground last Monday.
Earlier on Sunday, last year's runners-up Cardiff City held 10-times winners Arsenal to a goalless draw at Ninian Park.
Everton, still without a recognised striker and with midfielder Mikel Arteta a late withdrawal because of a rib injury, produced another well-drilled display to frustrate their fiercest rivals from the start.
Liverpool manager Rafa Benitez left striker Robbie Keane out of his matchday squad but Fernando Torres and Dirk Kuyt got little change from Everton's sturdy defenders.
That was not the case at the other end as, six days after Tim Cahill was left unmarked to head Everton's late equaliser, the spring-heeled Australian was again given a free header at a Steven Pienaar corner and Lescott's flick diverted the ball past Pepe Reina.
Unsurprisingly it was Gerrard, who shot his team ahead on Monday, who saved the day when he was sent through by a clever Torres backheel and scored with a low shot that Tim Howard should have saved.
SCRAMBLING DEFENCE
Howard produced a good block from the dynamic Gerrard soon afterwards and Everton were forced into scrambling defence in the last 15 minutes but, as so often this season, Liverpool's neat passing did not create enough Anfield danger.
Gerrard saw it differently. "In the league game Everton were worthy of a point but today we dominated for 90 minutes," he told Setanta Sports.
"I thought we were fantastic and if you look at chances you've got to be disappointed.
"But we go again, we are confident we can go there and win it," he said of the replay that will decide who hosts Aston Villa or Doncaster in the fifth round.
Cardiff enjoyed another satisfying day in what could be the last Cup game played at the ground that has been their home for 99 years.
The Championship side had good chances in the first half through Joe Ledley and Paul Parry, while Ross McCormack clipped the bar late on.
Arsenal took control in the second half but their dominance did not lead to many clear opportunities and when they did find a way through, Cardiff keeper Peter Enckelman kept everything out.
The winners of that replay will host West Bromwich Albion or Burnley.
In Saturday's action, holders Portsmouth were knocked out when they were beaten 2-0 at home by Championship Swansea, while Manchester United came from behind to beat Tottenham Hotspur 2-1 to earn a last-16 game away to either Nottingham Forest or Derby County.
