Chelsea won their third consecutive match in three different competitions after sweeping aside League One Walsall.
Ramires, Loic Remy and Kenedy, on his full debut, put the visitors in control before Pedro’s late strike secured a comfortable 4-1 win.
The competitive Saddlers pulled a goal back through James O’Connor before half-time but they could not cope with Chelsea’s power as the holders cruised into the fourth round.
They now head to Newcastle, a club in a real crisis following their cup exit to Sheffield Wednesday, in the Barclays Premier League on Saturday aiming to claw back the gap to Manchester City at the top.
Chelsea were occasionally tested by their Sky Bet League One hosts but the recalled John Terry, among eight changes for the visitors, and Jose Mourinho avoided the Banks’s banana skin.
Seven-goal Tom Bradshaw, who scored a hat-trick in Walsall’s first round win over Nottingham Forest, missed out with a groin injury meaning Jordan Cook started up front for the hosts.
And the Saddlers desperately missed Bradshaw as they lacked a focal point from the start.
Neil Etheridge, who spent four years at Chelsea as a scholar, twice saved from Falcao and Ramires inside the first four minutes as the visitors looked to kill off any threat early.
They dominated from the start, with Ruben Loftus-Cheek also seeing a shot blocked, before taking an inevitable early lead on 10 minutes.
Walsall were their own worst enemies, though, as they contrived to gift Chelsea the opening when Etheridge’s sloppy pass left Paul Downing in trouble and he was robbed by Kenedy.
The 19-year-old then had time to cross from the left for the unmarked Ramires to head in at the far post.
Chelsea were in no mood to let the Saddlers off lightly, with Falcao’s movement and Ramires’ drive causing problems and the duo combined after 20 minutes.
Ramires slipped Falcao through, and when Etheridge got a touch on his low shot, O’Connor hacked it off the line.
The Monaco loanee was making his first start for Chelsea and dominated O’Connor, with his touch and awareness too sharp, even if he failed to find the net.
But just as O’Connor struggled Branislav Ivanovic had his moments against the impressive Romaine Sawyers and former Chelsea forward Milan Lalkovic, who counts Nemanja Matic among his close friends.
The Saddlers had gradually grabbed a foothold following their sloppy start and Lalkovic fired wide after tricking his way past Ivanovic on 26 minutes while Sawyers’ marauding made life difficult for Chelsea’s right back.
Mourinho’s men, though, seemingly eased any concerns ahead of half-time as they doubled their lead four minutes before the break.
Again it was the impressive Ramires at the heart of the move as his slipped in Remy on the right and the forward’s first-time effort flew past Etheridge.
Yet Walsall handed themselves a lifeline in first-half injury time when Asmir Begovic parried Lalkovic’s 30-yard free-kick and O’Connor’s follow up crawled across the line.
It raised the decibel level at the Banks’s Stadium but they were silenced seven minutes after the re-start when Chelsea regained their two-goal lead.
The hosts were surprisingly subdued and paid the price when Loftus-Cheek threaded a delightful throughball for Kenedy to lash in from 10 yards.
A rogue sprinkler which went off in the corner briefly halted play but it failed to dampen Chelsea’s enthusiasm and Remy shot wide with 25 minutes left.
The Saddlers,though, refused to go quietly and Sawyers headed over as they mounted some late pressure without managing a scare.
And substitute Pedro wrapped up the game for Chelsea in stoppage time when he drilled in from the edge of the box.