Frank Lampard and Edin Dzeko each scored twice as City strolled to victory with seven second-half goals at the Etihad Stadium yesterday, setting up a home game with Newcastle United.
Lampard broke the deadlock in the 47th minute, tapping home a low cross from James Milner at the near post to score his second goal in two games following Sunday's equaliser against his former club Chelsea.
Dzeko turned in a Jesus Navas cross in the 53rd minute and Navas made it 3-0 with a jinking run and fierce shot a minute later.
"I really enjoyed that because tonight we saw the team that we were used to seeing last year," said City manager Manuel Pellegrini.
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Chelsea gave a first appearance of the season to goalkeeper Petr Cech and took a 25th-minute lead against Bolton when debutant Kurt Zouma lashed home after Gary Cahill's header was blocked at a corner.
Chelsea will visit fourth-tier Shrewsbury Town in round four.
- Dummett delivers Newcastle -
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Meanwhile, Tottenham Hotspur had to come from behind to win 3-1 at home to Nottingham Forest.