Arsene Wenger's side will meet Everton in the quarter-finals, but the French coach should thank referee Howard Webb for helping his team progress after the match official missed a blatant late challenge by Alex Oxlade-Chamberlain on Suarez on 63 minutes with Arsenal clinging on grimly to a 2-1 lead.
The home side had moved 1-0 ahead against the run of play when Oxlade-Chamberlain drove the ball into the net for the opening goal from a loose ball before Lukas Podolski added the second three minutes after the break with Oxlade-Chamberlain playing provider.
It was a minor miracle how Liverpool - who thumped Arsenal 5-1 in the Premier League a week ago - were behind, but Steven Gerrard gave them hope when he converted a penalty around the hour-mark after Podolski had made a clumsy late challenge on Suarez.
It was soft, but there was no doubt about the penalty that never was, with Oxlade-Chamberlain late on Suarez, who smiled in disbelief as Webb decided not to award the visitors another penalty.
Arsenal relied on goalkeeper Lukasz Fabianski to keep the visiting side at bay while Webb did Liverpool a favour by missing a Gerrard foul on Oxlade-Chamberlain that would have earned him a second yellow and a red card with 16 minutes remaining.
2' - STURRIDGE CHANCE: Chance for Sturridge, but his shot is saved by Fabianski. Terrific pass from Gerrard to pick out the striker. Liverpool almost in for the opening goal in the second minute.
4' - STURRIDGE BLOWS SECOND CHANCE: Sturridge goes beyond Fabianski from the Coutinho pass, but he can't wrap his right foot around the shot as the ball fires into the side netting. Mertesacker all over the place at the back.
16' - ARSENAL MOVE AHEAD: Gerrard blocks the volley by Sanogo, but Oxlade-Chamberlain follows up to slam the rebound under Jones. Arsenal lead 1-0 with their first real attack of the afternoon.
40' - FABIANSKI PRODUCES SUPERB STOP: Ball over the top of the Arsenal defence. Suarez drills the volley at goal, but Fabianski makes a handy stop in diving to his right to make the stop.
47' - MORE FABIANSKI HEROICS: Fabianski with a fine stop to make the stop from the Suarez shot with his right peg. Brilliant stuff from the Uruguay striker to go beyond Koscielny.
48' - PODOLSKI ADDS THE SECOND: Podolski buries the ball into the net from the Oxlade-Chamberlain pass. Fine finish beyond Jones. Arsenal lead 2-0 here.
52' - SUAREZ GOES CLOSE: Suarez lifts a volley inches over the bar. Superb pass from Gerrard, and terrific control by Suarez as the ball falls inches over the bar.
54' - JONES DENIES OZIL: Fine save by Jones to prevent Ozil from finding the net. That had some pace on it, but the goalkeeper produced a strong left handed stop.
60' - LIVERPOOL NET PENALTY: Podolski takes out Suarez from behind and Howard Webb points to the spot. Silly challenge by the German player. Gerrard sends Fabianski the wrong way from the penalty.
62' - STURRIDGE DENIED AGAIN BY THE HOME GOALKEEPER: Glorious chance for Surridge to level matters, but Fabianski is off his line to make a brilliant stop at the feet of the striker as he tried to round him.
64' - SUAREZ ROBBED OF EARNING ANOTHER PENALTY: Alex Oxlade-Chamberlain with a thumping challenge on Suarez in the box. Looked a clear-cut penalty, but the ball was away and there was a suggestion of Suarez running into the Arsenal youngster. No penalty.
73' - GERRARD AVOIDS RED CARD: Gerrard takes out Oxlade-Chamberlain. Clear foul, but Howard Webb settles for a corner when Gerrard should have been booked for a second time and sent off.
86' - AGGER HEADS WIDE WITH THE GOAL GAPING: Agger nods wide of goal from the Gerrard free-kick with Fabianski out of his goal. That really should have been the equaliser. What a chance. Just needed to hit the target.
Arsenal have only lost one of their last 37 FA Cup home games, winning 27 and drawing nine.
Olivier Giroud has been involved in five goals - three scored and two assists - in five previous FACup appearances.
Steven Gerrard's penalty ended a run of 695 minutes without conceding a goal at home for Arsenal.
Lukas Podolski has scored four times in four FA Cup appearances.
Alex Oxlade-Chamberlain has scored three goals his last three appearances for Arsenal at the Emirates.
TALKING POINT How bad was Howard Webb's decision not to award Suarez a penalty? An astonishing call really from a man who has officiated a World Cup final. He was only yards away from Oxlade-Chamberlain when he sent Suarez spinning up in the air. How he failed not to award Liverpool a penalty that could have given the visiting side the chance to level was a huge blunder. Even if he did even up the score by not sending Gerrard packing in the closing 17 minutes. They were both bad, bad decisions.
MAN OF THE MATCH
Lukasz Fabianski (Arsenal): The goalkeeper was the outstanding performer for his side. Made several excellent stops to prevent Liverpool from progressing. Liverpool won this fixture 5-1 at home a week ago, and would have scored five here without the performance of the Arsenal goalkeeper.
Arsenal: Fabianski 8; Jenkinson 6, Mertesacker 6, Koscielny 6, Monreal 5; Arteta 5, Flamini 5; Oxlade-Chamberlain 7, Ozil 6, Podolski 6; Sanogo 7...subs: Gibbs 6, Cazorla 6, Giroud 6
Liverpool: Jones 7; Flanagan 6, Skrtel 6, Agger 6, Cissokho 6; Gerrard 7, Allen 6, Coutinho 7, Sterling 7; Sturridge 7, Suarez 8...subs: Henderson 6
THE MATCH IN A TWEET