Mauricio Pochettino's men were bereft of attacking inspiration in the opening 45 minutes, but two headers from Armando Broja and Thiago Silva saw the Blues belatedly build up a healthy advantage before Raheem Sterling's free kick and Enzo Fernandez's tap-in put the icing on the cake.
Chelsea were one of two Premier League sides in action in the quartet of 5.30pm kickoffs, and Aston Villa needed a huge stroke of fortune to earn a 1-0 win over Middlesbrough, who succumbed to an 87th-minute strike from Matty Cash which took a wicked deflection off of Emmanuel Latte Lath.
Earlier in the day, Newcastle United came up trumps 3-0 over Sunderland in the Tyne-Wear derby, while Maidstone United produced one of the shocks of the day, sinking League One Stevenage 1-0 thanks to a Sam Corne penalty in first-half injury time.
Fellow Premier League outfits Brighton & Hove Albion, Sheffield United and Bournemouth also advanced to round four courtesy of away wins, with the Seagulls sinking Stoke City 4-2 despite initially going a goal behind.
Sheffield United make extremely light work of Gillingham, as William Osula and James McAtee both netted braces in a 4-0 win, while Bournemouth came from two goals down to sink Queens Park Rangers 3-2 thanks to a second-half flurry.
Few surprises were sprung elsewhere, although fifth-tier Eastleigh forced a replay with Newport County, holding the League Two side to a 1-1 draw despite playing the entire second half with 10 men, while Bristol Rovers and Norwich City played out their own two-goal stalemate.
Championship duo Hull City and Birmingham City will also require a rematch due to a 1-1 draw at the MKM Stadium, but Premier League-chasing Leicester City and Ipswich Town made it through, beating Millwall 3-2 and AFC Wimbledon 3-1 respectively.
Another all-Championship battle saw Sheffield Wednesday eliminate Cardiff City in a dominant 4-0 Hillsborough triumph, with the Owls netting three goals in the first 45 minutes before Mallik Wilks got in on the act in injury time.
Coventry City emphatically marched into the fourth-round draw owing to a 6-2 demolition of Oxford United, while Blackburn Rovers recovered from a slow start to demolish Cambridge United 5-2, thanks in no small part to a Sammie Szmodics hat-trick.
Ryan Fraser netted twice as Southampton crushed Walsall 4-0 at St Mary's, but Watford made extremely hard work of their 2-1 win over National League side Chesterfield, who were seconds away from a replay until Tom Dele-Bashiru struck in the fifth minute of second-half injury time.
In their first match since the appointment of Ian Foster as their new head coach, Plymouth Argyle ran out 3-1 winners over Sutton United, while Arsenal-owned Charlie Patino and Jerry Yates were on target for Swansea City in a 2-0 success over Morecambe.