Arsene Wenger's team was on the ropes in the early stages of a lively FA Cup tie, until Alex Oxlade-Chamberlain scored a goal against the run of the play. His strike shifted the momentum in the hosts' favour and he set up another for Lukas Podolski as Arsenal won 2-1 to advance to the quarterfinals on Sunday.
Following their 5-1 thrashing at Anfield in the Premier League, when they conceded four goals in the opening 20 minutes, the Gunners got their revenge after surviving another sustained period of Liverpool pressure in the second half.
They will next face Everton at home after the Toffees booked their place with a 3-1 defeat of Swansea, while Manchester City will face Cup holder Wigan in a rematch of last year's final.
"The intensity of the performance pleased me, I am very proud of the way we responded to the huge defeat that we had last week," said Arsenal manager Arsene Wenger, chasing his first piece of silverware since the 2005 FA Cup.
Liverpool again looked the stronger team in the early stages. A superb through ball from Steven Gerrard found Daniel Sturridge, but the England striker's low shot was parried away by keeper Lukasz Fabianski.
Luis Suarez's flicked pass then picked out Sturridge's run behind Per Mertesacker, but Fabianski forced him to shoot wide.
"I thought the best team lost. I thought the very least we deserved was a replay," Liverpool manager Brendan Rodgers said. "We probably should have been 2-0 up inside those first six or seven minutes. Going forward we were outstanding. I'm disappointed with the goals, the first one in particular was just a long ball into the box."
Though Arsenal struggled to keep the ball, Oxlade-Chamberlain put the home side ahead after Liverpool failed to clear a free kick. Yaya Sanogo, making his first start for Arsenal, saw his shot blocked by Gerrard but the ball rebounded for Oxlade-Chamberlain, who confidently slotted home from close range past Brad Jones in the 16th minute.
Arsenal was sharper on the ball after the goal but Liverpool remained dangerous on the break, with Suarez combining well with Sturridge on a swift counterattack.
Raheem Sterling then showed his speed and technique down the left flank, rounding Carl Jenkinson before his tired effort from a narrow angle was diverted away for a corner.
Suarez had two more opportunities to put his team level before halftime but Fabianski, having a superb game, dived well to deny his low shot before the Uruguay striker missed the target with a chip from the edge of the box.
Suarez went close immediately after the interval when he almost beat Fabianski with a low shot that forced the keeper into a fine reflex save.
Arsenal doubled its lead on the next move, a slick-passing counterattack concluded by Podolski, who scored with a clean finish from Oxlade-Chamberlain's cutback in the 47th.
Arsenal then had a good spell of possession but, after Suarez unleashed a powerful volley over the bar and Mesut Ozil threatened Jones with a low shot, the Uruguay striker won a penalty when Podolski clumsily clipped his ankle in the box.
Gerrard coolly converted from the spot to pull one back, sending Fabianski the wrong way in the 59th minute.
Suarez was jeered by Arsenal supporters when he went down after a hefty collision with Oxlade-Chamberlain in the box with 26 minutes to go. Referee Howard Webb ignored the visitors' appeals for another penalty.
Substitute Santi Cazorla should have restored Arsenal's two-goal lead in the 73rd when he thumped a volley far over the bar while unmarked from the edge of the box. Daniel Agger had Liverpool's best chance to make it 2-2 in the 87th minute, but his header following a free kick from Gerrard just drifted over the top.
At Goodison Park, substitute Steven Naismith scored a goal and won a penalty. With the score level at 1-1, Everton manager Roberto Martinez opted for experience when he made a double substitution on the stroke of the hour, with Naismith and Leon Osman replacing Lacina Traore and Ross Barkley.
The move paid off as Naismith took full advantage of Neil Taylor's back pass to slide the ball into the bottom corner in the 65th minute. Everton was then awarded a penalty after Jazz Richards fouled Naismith, with Leighton Baines converting.
Traore had put Everton ahead, back-heeling into the net from close range in the fourth minute before Jonathan de Guzman equalized.
Chris Porter scored twice in stoppage time as Sheffield United also advanced by beating Nottingham Forest 3-1. There will be a non-Premier League side in the semifinals as third-tier United will either take on second-division sides Sheffield Wednesday or Charlton Athletic in the last eight.