Goals from Michael Ballack, Salomon Kalou, Nicolas Anelka and Frank Lampard rescued the Blues after Adam Barrett had stunned them with a 15th-minute header in the third round replay - and eased the pressure on under-fire Scolari in the process.
The match, which was called off because of fog early in the evening and then declared 'on' again when it lifted, came just days after Chelsea had been beaten 3-0 at Manchester United.
And Southend looked set for an incredible upset following a goal that took full advantage of Chelsea's nervousness over set-pieces.
Scolari switched to a zonal marking system in a bid to end his team's defensive misery but his players looked all at sea as the Shrimpers won their first two corners of the match.
Petr Cech flapped the first one to safety but when Junior Stanislas whipped in the second the Blues defence stood completely still as the unmarked Barrett thundered home a header from 12 yards.
It was a nightmare start for the Premier League giants and it could have been worse if Cech had not produced a stunning save to prevent Alex Revell heading home a Stanislas cross later in the first half.
But with Southend fans singing 'You're getting sacked in the morning' and Chelsea supporters replying with 'It's so foggy, call if off' the Blues players finally found their manager a lifeline.
With seconds to go until half-time, Southend keeper Steve Mildenhall punched a clearance straight to Ballack and he volleyed home spectacularly from 25 yards.
When Kalou drilled home an angled shot on the hour mark the game was all but over and Anelka made sure, firing home from a Kalou pass in the 78th minute.
Lampard then curled home from the edge of the area in the 90th minute - making the final scoreline a little flattering because Southend had worked so hard and at one stage looked set for a memorable night.