Only Birmingham and Portsmouth must try again, against their Championship opposition of Nottingham Forest and Coventry respectively, but Manchester City, Everton and Tottenham all won.
Difficult, snowy conditions at the Riverside Stadium made conditions bad for both Middlesbrough and Manchester City, not that the visitor's minded, defeating their Championship opposition 1-0 with a strike from Benjani just on half time.
Financially troubled Portsmouth fell behind at Fratton Park to Coventry, but hit back on the stroke of half-time through Kevin-Prince Boateng to force a replay.
Burnley were 2-0 up by half time at MK Dons, with goals from Graham Alexander and Steven Fletcher, although Paul Ince's League One side did score a last minute consolation.
Nottingham Forest and Birmingham played out a goalless draw at the City ground as defensives stood firm. However, Robert Earnshaw did waste a golden opportunity to embarrass the visitor's when he blazed a second half penalty over the crossbar.
Managerless Bolton shrugged off losing their manager this week with a comprehensive thumping of League Two Lincoln 4-0 at the Reebok Stadium, all the strikes coming in the second half.
In the other all Premiership clash, Aston Villa recorded a 3-1 win over Blackburn, who had El-Hadji Diouf sent off in the first half for a lunging challenge on Habib Beye.
Rovers had a marvellous chance to draw level but David Dunne missed a penalty.
Both side's will now change their attention to their Carling Cup semi-final next week and named changed sides.
Everton meanwhile made hard work of seeing off League One side Carlisle at Goodison Park before eventually recording a 3-1 win.
Fulham go through to the next round thanks to a 1-0 hone win over Swindon Town and it was their in-form striker Bobby Zamora who scored the only goal.
The other all Premiership clash saw strugglers Hull and Wigan meet at the DW Stadium and despite the Tigers leading at half time, it was Wigan who roared back after the break to win 4-1.
York had their two minutes of fame as they took the lead against Stoke City before the Potters rallied to beat the non-league outfit 3-1.
The game had been delayed by half-an-hour due to the visitors' coach being held up in traffic due to the bad weather conditions.
Tottenham eased into the fourth round after a convincing 4-0 victory over Peterborough United at White Hart Lane as Niko Kranjcar scored twice.
Jermain Defoe netted on 70 minutes and Robbie Keane converted a last-minute penalty.
Sunderland ensured there were no upsets at the Stadium of Light as they disposed of Conference side Barrow 3-0.
