With a place in the last 16 already secured, City were below par at the Etihad Stadium and were twice pegged back by the Czech minnows.
Sergio Aguero and Samir Nasri both put Manuel Pellegrini's men ahead but Tomas Horava and Stanislav Tecl responded, before Negredo and Dzeko finally clinched victory in the last 12 minutes.
Pellegrini had made seven changes for the match - including restoring England goalkeeper Joe Hart - but it needed the late introduction of Negredo to finally tilt the game their way.
Dzeko, who had laboured for little reward, put the game beyond doubt in the last minute, setting up a potential group decider with Bayern Munich next month.
The victory was all that City required but the performance of some of the players brought in, and the defence in general, will be a cause for concern for Pellegrini.
City started brightly before some all-too-familiar sloppiness at the back, in the continued absence of captain Vincent Kompany, allowed Plzen to grow in confidence.
But on the issue of Hart's return, after five games on the bench, the goalkeeper could at least be pleased with his efforts after making a couple of good saves.
Javi Garcia stabbed City's first chance wide after five minutes when he was picked out by Samir Nasri at a set-piece.
Nasri, in fine form of late, then hit the bar for a second successive game with a thunderous effort from 25 yards.
The Frenchman was presented with an easier opportunity when Aguero deftly floated a cross to the far post but he sidefooted a volley wide.
Aguero then skipped past two challenges to fire wide before Hart passed his first examination by confidently claiming a corner.
Hart's quick thinking also almost led to the opening goal as he immediately released the ball and Aguero raced through to fire home, only to be pulled up for a foul.
That decision seemed harsh but the hosts were perhaps fortunate to be awarded a penalty just after the half hour when Aguero's cross struck Frantisek Rajtoral's hand.
Aguero confidently dispatched the spot-kick for his 15th goal in his last 12 appearances.
It was hoped the goal might ease a few jitters that had become apparent in the City defence in the minutes preceding it.
Most notably, Rajtoral had shot wide at the end of a slick move from the Czechs moments earlier.
But it appeared to have the opposite effect as, for the remainder of the first half, Plzen started to take the game to the hosts.
Plzen were even down to 10 men for a spell as Roman Hubnik received treatment following a clash with a team-mate but still threatened again through Rajtoral.
This time Aleksandar Kolarov, captain for the night, saved City with a good block.
Plzen enjoyed more good possession and an equaliser came two minutes before the interval as Horava unleashed a fierce shot from distance that gave Hart no chance.
The equaliser was probably deserved but although City looked to respond in the second half, perspective was offered as Aguero was withdrawn and Jesus Navas sent on.
Kolarov shot wide from a free-kick after Nasri was fouled and Fernandinho forced Matus Kozacik to tip over with a powerful header.
That proved the Brazilian's final act as Yaya Toure replaced him soon after, and City reclaimed the lead just after the hour when Nasri volleyed in from a Navas cross.
Again, City's expected cruise to victory did not occur as Plzen came forward again.
Hart did wonders for his confidence with a fine save from a long-range Daniel Kolar strike but it did not repel the Czechs for long.
More uncertainty at the back was exploited and Kolar set up Tecl to score from close range.
It might have got worse for City when Martin Demichelis brought down Kolar on the edge of the area but Pavel Horvarth shot over.
City sent on their other in-form striker, Negredo, for Nasri with five minutes remaining and he soon made an impact.
In truth he could not miss, as he found himself in the right position when Navas' cross was diverted his way by Dzeko, who may have been disappointed not to score himself.
Still Plzen were not done and Hart came to their defence again to deny Rajtoral with his feet.
Dzeko got his goal in the dying moments when he nodded in a cross from a James Milner cross.
Source: Manchester City MAD