A strong Chelsea line-up began with gusto and seemed intent on erasing memories of their Carling Cup humiliation and the difficult replay against Southend in the previous round of this competition.
Chelsea full-backs Cole and Jose Bosingwa were getting plenty of space to surge forward down the flanks, with the England defender instrumental in the opening goal.
Lampard found his England colleague, who was acting more as a left-winger, and Cole then cut the ball back to Ballack who atoned for an earlier miss to give Chelsea the lead.
Bizarrely, considering Chelsea's experiences with lower-league opposition in cup competitions this season, the Blues then took their foot off the pedal and were made to pay.
Chelsea's inability to deal with set-pieces came to the fore again as Owen Garvan's free-kick found the unmarked Bruce at the back post and the defender hit home to level matters.
That goal sparked an Ipswich resurgence as Danny Haynes and Tommy Miller both went close to giving the visitors the lead before the break.
But Ipswich were made to rue their first-half profligacy when Ballack bent his free-kick over the defensive wall for his second after Garvan had felled Nicolas Anelka.
Unlike the first half, Chelsea continued to attack after going ahead with Salomon Kalou forcing a fine save from Wright.
Two minutes later Ballack came close to claiming his hat-trick with a 25-yard shot which was palmed away by Wright.
Chelsea were playing high-tempo football, with Lampard instrumental in midfield - and the England international capped off a fine performance with a stunning strike to rubber-stamp his team's progress.
Chelsea assistant coach Ray Wilkins on Michael Ballack:
"It was very doubtful whether Michael would make it. He took a nasty kick in training, he was scanned on Friday and was very doubtful.
"He turned up still feeling extremely sore, but he really wanted to play. When he goes forward he is extremely dangerous and the work he puts in for the team is untouchable.
"It was a really tough game for us but I felt that on the chances we created, we deserved to win it."
Ipswich boss Jim Magilton:
"This result won't define our season.
"We had some really good opportunities and played better in the first half. We scored a good goal from a set-piece and I am very pleased with the players overall.
"Chelsea have got world-class players and when you give them opportunities on the edge of the penalty box, they will hurt you and that is what they did."
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