City were no match for their hapless opponents, with the game all but over as a contest before half-time.
David Silva opened the scoring in the sixth minute and Sergio Aguero doubled City's lead midway through the half, with Magpies defender Steven Taylor seeing red before half-time.
A superb Yaya Toure free-kick put City 3-0 up five minutes after the break, while Samir Nasri put the gloss on the result in the 75th minute.
It was an exemplary performance from City, who are among the frontrunners for the Premier League crown this season, which will have no doubt thrilled their new manager Manuel Pellegrini.
Dzeko said: "I think we played a fantastic match and not only 45 minutes but 90 is what the manager expects from us.
"We played the first game at home and we wanted to show everyone what we are capable of.
"We scored four goals and we could have scored more but we are happy with these four.
"I wanted so badly to score but at the end, we won the game, we have three points and we have scored four."
While he did not manage to get on the scoresheet, Dzeko played an eyecatching role and the Bosnian striker was quick to hail Pellegrini's influence.
"The new manager brings something different to us, especially to me; giving me the confidence and that's what I needed," he added on Sky Sports 1.
Toure was also quick to salute a great team performance.
"I think it was a fantastic result, fantastic beginning. I want to continue like that because the Premier League is very, very tough," he said.
"We played very well, full credit to all the team, we worked really hard and we tried to kill off the game in the first half."
Pellegrini was impressed with his new side's performance over the course of the 90 minutes.
The Chilean, who left Malaga over the summer to replace Roberto Mancini in the City hotseat over the summer, said: "For me the most important thing is the way we played for 90 minutes. We didn't play one way when we were winning, we tried to play football for 90 minutes; attacking and defending.
"We scored four goals, I think we had at least six or seven chances to score more and we didnt concede any goals."
The former Real Madrid boss was also effusive in his praise of Spain winger Jesus Navas and Brazilian midfielder Fernandinho, both of whom excelled in their first competitive game for City.
"I said before the match that both of them are very important players for us," added Pellegrini.
"Navas always plays wide and he gives a lot of passes inside the area, and Fernandinho works the 90 minutes with the ball and without the ball.
"I'm very happy with the way they played."