The managerless visitors proved ideal cannon fodder for Carlo Ancelotti's faltering double winners, who went into Sunday's game on their worst Premier League run for almost 15 years.
Ancelotti's decision to continue last season's policy of fielding some youngsters in the early rounds of the cup did not backfire, with Daniel Sturridge and Frank Lampard scoring twice, Salomon Kalou also finding the net and Nicolas Anelka ending the personal goal drought that has coincided with Chelsea's two months of misery.
Ancelotti, who handed rare starts to 17-year-old Josh McEachran and 20-year-old Patrick van Aanholt, will be praying Sunday's win helps inspire his established stars, like the rested Didier Drogba, Florent Malouda, Michael Essien and Ashley Cole, to kick-start their ailing league campaign.
Despite the number of changes and standard of opposition, Chelsea - looking to become the first club to win a hat-trick of FA Cups since the 1880s - continued to be dogged by a lack of cutting edge in the opening half-hour.
Sturridge, rewarded with a start after scoring five times for the reserves on Thursday, saw one chance closed down by Marton Fulop and another balloon off target.
They were almost made to pay by the team who had boss Roy Keane sacked on Friday.
A fine break involving Scotland and David Norris ended in the former unleashing a left-footed piledriver which Petr Cech could only beat away.
Chelsea surged down the other end and Anelka looked to have put them ahead but Troy Brown produced a brilliant clearance off the line from the Frenchman's low finish.
Lampard blasted over after good work down the left from Van Aanholt and McEachran's drive was deflected behind off Connor Wickham.
A lovely Chelsea move was then spoilt by a horrible finish from Anelka, who made amends by providing the breakthrough in the 33rd minute after Ipswich gave the ball away in midfield.
Chelsea sprung forward and Anelka's finish hit Fulop and squirmed towards the line before Kalou made sure.
It was 2-0 less than a minute later, Sturridge tucking home Jose Bosingwa's low cross after more poor defending from the visitors.
Lampard's weak 20-yard shot was straight at Fulop as Chelsea looked to kill off the tie before half-time.
Ipswich captain David Norris was booked for a poor tackle on John Terry and Lampard made him pay from the resulting 41st-minute free-kick, with Carlos Edwards flicking the ball into his own net.
Anelka's mis-hit finish was straight at Fulop at the start of the second half but the striker finally ended his barren spell in the 49th minute, finding the bottom corner after a neat exchange with Kalou.
Ipswich had been preparing a substitution at the time and immediately withdrew Scotland for Ronan Murray.
Chelsea began to play with a swagger and Sturridge made it 5-0 three minutes later, curling superbly into the top corner from just inside the box.
Ancelotti threw on another youngster, with Gael Kakuta replacing Kalou.
Peters drilled wide in search of a consolation before the highly-rated Wickham was replaced by Tamas Priskin.
Chelsea lost Van Aanholt to injury for the final 20 minutes, with Jeffrey Bruma entering the fray.
The home side were in cruise control but Ipswich pressed the self-destruct button again twice in a minute to hand Lampard a quickfire double.
The England midfielder blasted home from 15 yards after the visitors failed to clear a corner, and then bundled home Branislav Ivanovic's low cross.
It was party time at Stamford Bridge and Ramires fired over with the outside of his right foot before Chelsea fans showed their support for the under-pressure Ancelotti, who responded with a wave.
Kakuta, Anelka and Ivanovic all had chances to make it 8-0 in stoppage-time before the final whistle ended Ipswich's torture.