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
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