Arsenal needed extra time and penalties to beat second division Sheffield United, England defender Ashley Cole converting the decisive spot-kick to win the shootout 4-2 following a goalless draw.
Striker Peter Crouch scored twice to help Southampton beat third division Brentford 3-1, and Blackburn's Morten Gamst Pedersen lashed in an 86th-minute winner to seal a 2-1 victory over local rivals Burnley.
Southampton will entertain holders Manchester United in the last eight, Arsenal travel to Bolton Wanderers and Blackburn host second division Leicester City.
Second division Nottingham Forest play Tottenham Hotspur in the last fifth-round replay on Wednesday with the winners travelling to Newcastle United in the quarter-finals on March 12 or 13.
Sheffield United forward Michael Tonge missed a golden opportunity to put his side ahead in the opening minute against Arsenal when he blazed the ball wide from just two metres out with the goal gaping.
The champions dominated the rest of the match, midfielder Francesc Fabregas hitting the crossbar in the second half, but their goalkeeper Manuel Almunia had to make a fine save in stoppage time to deny United defender Jon Harley.
SEVERELY DEPLETED
Arsenal, severely
In the shootout, Arsenal's Lauren, Patrick Vieira, Freddie Ljungberg and Cole held their nerve to score, and Almunia produced good saves from Alan Quinn and Harley to put the London side through.
"It was a really tough game and you must give a lot of credit to Sheffield United," Vieira told Sky Sports. "But we always produce when our backs are against the wall and we are really happy to be in the next round."
Brentford took a shock lead after four minutes against Southampton through midfielder Eddie Hutchinson, only for Crouch to level seven minutes later.
The third division side had chances to restore their advantage but experienced forward Kevin Phillips put the visitors ahead from close range on 67 minutes and Crouch wrapped up victory in stoppage time.
Southampton face Manchester United in the quarter-finals, a repeat of the 1976 FA Cup final in which the Saints produced a huge upset with a 1-0 victory.
Pedersen was Blackburn's hero against neighbours Burnley, sealing victory with a venomous strike from a narrow angle.
Blackburn's Turkish midfielder Tugay had put his side ahead with a deflected shot but Micah Hyde equalised for Burnley just before halftime with a spectacular effort from the corner of the penalty area.
