Chelsea banished any fears of a repeat of last season's shock FA Cup fourth-round exit when they crushed Championship side MK Dons 5-1 to reach the fifth round.
Everton comfortably won 3-0 at fourth tier Carlisle United in the early kickoff, with the fourth-tier club playing at home for only the second time after floods damaged their Brunton Park home in December.
A first half hat-trick by Brazilian Oscar put Chelsea in command by halftime thanks to a tap-in after 15 minutes and two superb strikes after 32 and 44 minutes.
Chelsea dominated the game with 15 shots on goal in the first 45 minutes.
Eden Hazard, who had not scored for 30 matches, made it 4-1 from the penalty spot after 55 minutes before substitute Bertrand Traore, who had been on the pitch five minutes, scored his first goal for Chelsea to make it 5-1 in the 62nd.
MK Dons, who defended poorly in an entertaining match, got a brief glimmer of hope after 22 minutes when former Liverpool midfielder Darren Potter scored with a long-range shot that looped over Chelsea keeper Thibaut Courtois after taking a deflection off Nemanja Matic.
But MK Dons never looked like emulating the achievement of League One Bradford City, who won 4-2 at Chelsea at this stage of the competition last year after trailing 2-0.
Carlisle's hopes of an upset were doused within two minutes of kickoff as Arouna Kone tapped home the simplest of goals after Aaron Lennon swept down the right and sent in a low cross.
When the rampant Lennon cut past a static defender to fire in a second goal after 14 minutes, a long afternoon looked in store for Carlisle but they held out until a brilliant 65th minute Ross Barkley strike from the edge of the area made it 3-0.
Police afterwards said they were investigating allegations of racist chanting from a section of the home fans following Everton's first goal scored by Ivory Coast forward Kone.