Ipswich and Bournemouth also through.
Premier League champions Manchester City survived a huge FA Cup fourth-round scare as Kevin De Bruyne came off the bench to secure a 2-1 win at third-tier Leyton Orient on Saturday.
A wretched season for Pep Guardiola's side looked like reaching a new low as Orient protected a 16th-minute lead given to them by Jamie Donley's long-range wonder-strike that went in via the crossbar and the back of City keeper Stefan Ortega.
City huffed and puffed in response and were relieved when Abdukodir Khusanov equalised in the 56th minute, deflecting in Rico Lewis's shot.
De Bruyne came on late in the game and City's playmaker spared his side extra time when Jack Grealish played him in to score from close range in the 79th minute.
Even then Orient almost equalised when skipper Dan Happe volleyed over a great chance at the death.
Some lament the FA Cup losing its romance in recent years but this old-school tie had it in bucket loads.
A murky, drizzly lunchtime in an east London suburb lined with rows of Victorian terraced houses looked the perfect stage for Orient to ambush City's slickers.
While City lived to fight another day, it was a mightily relieved Guardiola who applauded the home fans at fulltime -- the same ones who chanted "you're getting sacked in the morning" to the serial trophy winner as his side were trailing.
"We played a really good game, it was a typical FA Cup game -- that's why this competition is unbelievable," Guardiola said.
"We behaved really well and reacted with character."
Orient, sixth in League One after a sensational run of form under Manchester United-supporting manager Richie Wellens, ran themselves into the ground.
And Tottenham Hotspur loanee Donley's goal -- despite being credited to Ortega -- will live long in the memory.
"I know I hit the goal well. I knew it fell for me nicely. I saw him off his line and luckily it went in," he said. "It would have been a lot nicer if we won," Donley said.
City made eight changes from last week's mauling across the capital at Arsenal but their line-up was packed with hundreds of millions of pounds' worth of talent.
Nico Gonzalez and Vitor Reis both made their debuts while Ruben Dias returned in defence with Grealish and Ilkay Gundogan adding experience.
Gundogan should have settled City's nerves when he somehow steered a Savinho cross wide with the goal gaping.
Orient, roared on by a capacity 9,000 crowd, were soon in dreamland as Gundogan lost the ball near the halfway line and the 20-year-old Donley spotted Ortega off his line and sent a long-range shot arcing goalwards.
Ortega back-pedalled, seemingly in slow motion, but could only push the ball against the crossbar before it hit his back and rolled in, sparking delirium around the stadium and on the balconies of the apartments wedged into each corner.
City's response was sporadic as Orient's young keeper Josh Keeley, also on loan from Tottenham, continued his remarkable FA Cup adventure. He headed a stoppage-time equaliser in the second-round win against Oldham Athletic and starred in the penalty shoot-out win over Derby County which earned the Os a date with City.
Keeley denied Omar Marmoush and Gundogan with superb stops but was helpless when Lewis's shot deflected off Khusanov to leave him wrong-footed. Guardiola sent on Phil Foden and De Bruyne and the changes paid off as Grealish fed De Bruyne to dink home.
Keeley went up for a late corner but there was no repeat of his Oldham heroics as Orient's dream run ended.
"Were we going to win the FA Cup? No. Can we win promotion? Yes," said a philosophical Wellens, whose side host Mansfield Town on Tuesday as they seek to reach the second tier for the first time since 1982.
City, meanwhile, turn their thoughts to Tuesday's Champions League playoff against Real Madrid.
The Premier League's bottom club Southampton lost 1-0 at home to Championship promotion hopefuls Burnley but fellow strugglers Ipswich Town enjoyed a confidence-boosting 4-1 victory at second-tier Coventry City managed by Frank Lampard.
Bournemouth's fine season continued as the won 2-0 at Everton in an all-Premier League clash while Fulham moved through to round five by beating third-tier Wigan Athletic 2-1 with Rodrigo Muniz scoring both goals for the London club.
Marcus Edwards scored on his Burnley debut as Southampton's woes continued. The forward joined from Sporting on loan on deadline day and made an instant impact, grabbing the winner 18 minutes after coming off the bench.
Ipswich reached the fifth round for the first time since 2007 despite making 11 changes to their side at Coventry.
George Hirst put Ipswich ahead with a penalty before Joel Latibeaudiere levelled but Jack Clarke's double put the visitors in control before halftime and Jaden Philogene wrapped it up after the break.
Championship leaders Leeds United were surprisingly beaten 2-0 at home by Millwall.
Everton's defeat by Bournemouth, for whom Antoine Semenyo scored a penalty and Daniel Jebbison doubled the lead, was the last FA Cup tie at Goodison Park before they move out of their home since 1892 to their new Bramley-Moore Dock home.
Holders Manchester United beat Leicester City on Friday and later on Saturday Newcastle United are at third-tier leaders Birmingham City and Chelsea visit Brighton & Hove Albion.