Goals from Michael Ballack, Salomon Kalou, Nicolas Anelka and Frank Lampard gave Chelsea, with only one win in their previous six matches, a deserved win after League One Southend had taken a shock 16th-minute lead with an Adam Barrett header.
The ultimately emphatic nature of the victory -- albeit against opposition 56 places below them on the league ladder -- was just the boost Brazilian coach Scolari needed after a recent run of unimpressive performances.
The only blot on the night for Chelsea was a bad knee injury suffered by Joe Cole and he could be sidelined for several weeks.
Hull City also made it through to the last 32 when they won the all-Premier League replay 1-0 against Newcastle United at St James' Park with an 81st minute tap-in from Daniel Cousin.
Newcastle manager Joe Kinnear and Hull counterpart Phil Brown were sent to the stands in the first half after squaring up to each other on the touchline.
Crystal Palace earned a trip to fellow Championship side Watford in the next round after they beat League One leaders Leicester City 2-1 at Selhurst Park with Paul Ifill and teenage substitute Sean Scannell scoring Palace's goals.
FOG CLEARS
Chelsea set up a fourth-round meeting with Ipswich Town of the Championship after taking control of the game which at one point in the evening was called off by referee Chris Hoy because of fog.
However, seven minutes after he took that decision, the fog lifted at Roots Hall and he allowed the match to go ahead in clear, perfect conditions.
Southend were initially very pleased he did, taking a shock lead when Barrett exploited a weakness in Chelsea's new zonal marking system to power in a header after 16 minutes.
Southend almost made it 2-0 20 minutes later when the zonal system failed again and Alex Revell headed straight at Chelsea keeper Peter Cech.
Ballack put Chelsea back in the match seconds before halftime with a well struck goal after a Southend mix-up before Kalou and Anelka added further goals in the second half.
Lampard's close-range effort in stoppage time completed the comeback.
"We need to organise a bit better. It's one of those things you go through from time to time. I'm sure by the weekend we will get it right," said Chelsea skipper John Terry.
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