Newcastle were incensed that a stunning volley from 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.
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.
City moved on to 47 points from 21 league 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 knjury after a clattering from defender Mapou Yanga-Mbiwa who was booked for the challenge.
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.