Rafa Benitez's Blues eased past Saints at St Mary's as Ba bagged a brace on his debut.
The Saints went ahead in the 22nd minute, Jason Puncheon slipping the ball through to Jay Rodriguez who ran on to the pass.
However, Ba scored 10 minutes before the break. Eden Hazard made his way down the left and threaded the ball through to Juan Mata whose shot from an acute angle was followed in by Ba.
The Blues took the lead on the stroke of half-time, Ashley Cole and Victor Moses enjoying a fine exchange before the latter fired home.
Chelsea all but confirmed progress with a third goal through Branislav Ivanovic who headed home Mata's cross (52).
Ba made it four (61) and Frank Lampard completed the scoring with a late penalty (83).
There were four shocks on Saturday, with non-league Luton and Macclesfield taking the plaudits along with Brighton and Oldham.
Two goals in the last five minutes by Matthew Barnes-Homer saw Conference side Macclesfield claim a 2-1 win over Championship leaders Cardiff.
The Bluebirds went ahead when Nathaniel Jarvis forced the ball home from close range but Macclesfield levelled when Barnes-Homer slotted into the centre of the goal with five minutes to go.
The game was turned completely on its head when Barnes-Homer scored from the penalty spot with two minutes to go after he had been fouled by Jarvis.
Luton had to endure nine minutes of injury time to send Wolves out of the competition.
Alex Lawless fired the Hatters ahead just 34 seconds into the second half as he lashed an unstoppable volley home at Kenilworth Road.
The first match of the third round saw an upset too as Premier League Newcastle went out 2-0 to Brighton at the Amex Stadium.
The Seagulls repeated last season's cup heroics by dumping an under-strength Magpies out of the competition with Andrea Orlandi supplying an outstanding opener.
The first-half strike was born out of Wayne Bridge's willingness to chase a seemingly lost cause, but it was Orlandi's touch, turn and fine shot that stole the show.
The second was delivered by substitute Will Hoskins, who tucked home David Lopez's defence-splitting pass, as the play-off hopefuls completed a comfortable win.
Newcastle were further frustrated by captain Shola Ameobi's second-half sending off.
Ameobi was deeply unlucky to receive the second yellow from referee Lee Probert and will miss Saturday's match against Norwich.
At the City Ground, Robbie Simpson scored twice as League One Oldham won 3-2 against Nottingham Forest.
Matt Smith's 13th-minute own goal put the hosts in front but the Latics levelled with a shot from distance by Simpson.
Simpson headed home four minutes later and things got worse for Forest.
Danny Collins was given a straight red card for a foul on Matt Smith and from the resulting free-kick, Jose Baxter made it 3-1. Billy Sharp scored in stoppage time but Oldham held on.
Bournemouth had to settle for a replay against Wigan after a 1-1 draw at the DW Stadium
The League One side took the lead four minutes before the break thanks to a fine goal by Eunan O'Kane.
However, the Premier League side levelled through a fortuitous penalty with Jordi Gomez's spot-kick parried by the keeper but the midfielder pounced on the rebound to slot home with 20 minutes left.
A stoppage-time goal by Nick Proschwitz saw Hull scrape a 1-1 draw against Leyton Orient at the KC Stadium.
The League One side went ahead with 12 minutes to go when Dean Cox's cross was met with a bullet header by David Mooney.
However, Proschwitz's downward header earned a replay for the Championship high-flyers.
Fulham needed an equaliser 10 minutes from time to earn a 1-1 draw at home to Blackpool.
Ludovic Sylvestre put the Seasiders ahead with half an hour to go when he fired home a 25-yard shot.
However, Robert Harris' clearance from Bryan Ruiz's corner could only find Giorgos Karagounis on the edge of the box and he looped a volley into the net.
Sunderland came from two goals down to claim a 2-2 draw at Bolton.
The Trotters went ahead in the 12th minute following a defensive mistake by Carlos Cuellar, his ball pounced on by Chung-Yong Lee whose low shot went into the centre of the goal.
Poor defending again saw Bolton double their lead as Marvin Sordell slotted home into the bottom left-hand corner from close range.
Connor Wickham gave Sunderland hope just a minute after coming on (60) and Craig Gardner sent an unstoppable equaliser into the roof of the net from 35 yards with 15 minutes left.
Aston Villa came from behind to beat Ipswich 2-1.
Michael Chopra pounced just after the half-hour for the visitors but Villa made a perfect start to the second half, Darren Bent stabbing home after good work by Charles N'Zogbia just 36 seconds after the break.
Gabriel Agbonlahor put a fine ball in which found Andreas Weimann who powered home a header to give Villa the lead with seven minutes to go.
Manchester City were also never threatened as they beat Watford 3-0.
Carlos Tevez, Gareth Barry and debutant Marcos Lopes got the goals.
Reading came from a goal down after 14 seconds to win 3-1 at League One Crawley.
Nicky Adams fired Crawley ahead but two from Adam Le Fondre and a Noel Hunt strike saw the Royals through.
Norwich eased to a 3-0 victory at Championship Peterborough.
Elliott Bennett put the Premier League side ahead after half an hour following Robert Snodgrass' pass and they doubled their lead four minutes before the break, Simeon Jackson getting in behind the defence.
Snodgrass got a third with 20 minutes left.
Clint Dempsey and Gareth Bale tormented Coventry as Tottenham eased to a 3-0 win at White Hart Lane.
In an all-Premier League clash, QPR and West Brom drew 1-1.
Shane Long put the Baggies ahead with a low shot with 11 minutes to go before Kieron Dyer levelled in injury time.
Crystal Palace and Stoke shared a 0-0 draw at Selhurst Park.
Hastings' on-loan goalkeeper Liam O'Brien saved a penalty from Ishmael Miller before Middlesbrough went on to win 4-1.
Merouane Zemmama (two), Andrew Halliday and Miller scored for Boro with Bradley Goldburg on target for Hastings at the Riverside.
Leeds and Birmingham drew 1-1, Huddersfield won 1-0 at Charlton who had Dorian Dervite sent off, Blackburn beat Bristol City 2-0 and Barnsley won 1-0 against 10-man Burnley.
Danny Hylton scored a hat-trick and was then sent off for serious foul play as Aldershot beat Rotherham 3-1 with both sides finishing with 10 men, Leicester won 2-0 over Burton, Derby eased past Tranmere 5-0, Sheffield United won 3-0 at Oxford and Sheffield Wednesday drew 0-0 with MK Dons.
Millwall beat Preston 1-0 while Southend drew 2-2 with Brentford.
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