After being held to a surprising draw 11 days ago, City proved far too strong for Blackburn with Negredo bagging his 20th and 21st goals of the season in two minutes either side of halftime before strike partner Edin Dzeko got in on the act.
His two goals came either side of one from Sergio Aguero, who netted a minute after coming on for his first appearance following a month-long injury absence.
Last season's beaten finalists City will face Watford at home in the fourth round.
"I don't think it was easy," Dzeko told ITV. "Especially, in the first half.
"The first goal was very important for us as well as the goal at the start of the second half. And as usual we then scored some more."
City fans who expected another goal-scoring procession would have been disappointed by a largely unexciting first half in which Blackburn dug in, with little ambition to break.
The hosts made eight changes to their side and while the five-times Cup winners still fielded a stellar cast, without the injured Samir Nasri, string-puller David Silva and powerhouse Yaya Toure they lacked creativity in midfield.
City's passing and decision-making were sub-standard and chances were scarce before the hosts broke the deadlock in first-half stoppage time.
Negredo had been a willing runner up front and was rewarded with his 20th goal of the season, a towering header on the run after Fernandinho had whipped and excellent cross to the far post in a rare moment of quality.
The striker's 21st of the season arrived two minutes after the break, a neat finish from halftime substitute Aleksandar Kolarov's fantastic crossfield pass, with Negredo flicking the ball over Blackburn's advancing keeper with the outside of his left boot.
Dzeko's first goal on 67 minutes made the game safe and was an equally stylish finish with the Bosnia striker swivelling in the area to rifle Jesus Navas's near post cross into the top corner.
City are not in need of striking reinforcements, but Aguero came off the bench to bolster the attacking options and found the net immediately with a low finish before Dzeko added the final flourish with another near-post effort 10 minutes from time.
City, who took their goalscoring tally to 99 for the season, are still competing on four fronts and Dzeko feels they are stronger than when they won the Premier League title in 2012.
"We have a few more world-class players, like Fernandinho, (Jesus) Navas and Negredo. Of course that is why we are better," he said.
"We are still there for four trophies but our target is just to win the next game."
