Newcastle were incensed that a stunning volley from Ivorian international midfielder Cheick Tiote was disallowed by referee Mike Jones after 34 minutes when the hosts trailed 1-0.
Tiote smashed the ball home with a swerving 20-metre left-foot shot, but, as the Newcastle players were celebrating, the referee consulted with his linesman and disallowed the goal.
They decided that Yoan Gouffran, who was standing in an offside position three yards from goal, was interfering with play and blocking goalkeeper Joe Hart's line of vision.
Tiote, who has only scored one goal for Newcastle in 104 appearances, told the BBC: "I think it was a goal and I don't know why the referee didn't accept it.
"We asked the referee to explain why he didn't give the goal, but he didn't say anything so we had to get on with it."
United manager Alan Pardew told Sky Sports he also did not know why the goal was disallowed as he felt Hart's vision was not impaired.
"The referee has not been clear in his answers. I don't understand it. Even if Man City's defenders were on the edge of the box and we'd have had four offside, its such a clean hit it was going in the top corner so there was no way Gouffran was in Joe's view.
"Unfortunately that was a massive call and he has denied it on a tiny technicality here which I think was wrong. It had an impact because we were so frustrated and could not have played any better."
PERFECT RUN
Dzeko swept City into the lead after eight minutes, timing his run perfectly to meet a cross from Aleksandr Kolarov to plant the ball past Tim Krul.
Their second came in the final seconds when Negredo beat the offside trap and scored at the second attempt after his first effort was blocked by Krul for City's 94th goal of the season in all competitions.
"It was a very difficult game and it's a very big result as we know it's a tough place to come and win," Manchester City boss Manuel Pellegrini told the BBC.
"It was an offside goal as they were interfering with Joe Hart and the referee made that call," he added of Tiote's strike.
City moved on to 47 points from 21 matches, one ahead of Chelsea. Arsenal, who started the weekend top, will go back to the summit if they win at Aston Villa on Monday.
The one blot for City was seeing Frenchman Samir Nasri carried off on a stretcher in the later stages with what appeared to be a serious knee injury after a clattering from defender Mapou Yanga-Mbiwa who was booked for the challenge.
"I think the tackle on Nasri should have been a red card," added Pellegrini.
It was City's 10th successive win over Newcastle in all competitions and the third time they have beaten them this season after a 4-0 win at the Etihad on the opening day of the season and a 2-0 win at St James' Park in the Capital One (League) Cup in October.
The Magpies have now lost three successive league games and are eighth in the table with 33 points.
In the day's other match, Liverpool were playing at Stoke City.
