Dzeko was among the goalscorers as City ran out 5-0 victors at the Etihad Stadium - their biggest win of the campaign - to cut Chelsea's lead at the top of the Barclays Premier League to five points.
City netted 102 goals in winning the competition last year but have been well below that exhilarating standard this term, and questions were asked of their durability during a recent poor run.
Manuel Pellegrini's men went four games without a league win early in the new year, allowing Chelsea to stretch ahead, but a 4-1 win at Stoke, followed by Saturday's success, has changed the mood.
Dzeko said: "I think the first half was maybe one of the best this season
Recently maybe we didn't play the best football, didn't score so many goals, but in the last two games we scored nine and hopefully we are back to normality - like we played last season
We have to continue."
City needed just 24 seconds to take command of the game, as the highly impressive Dzeko seized on a mistake by Vurnon Anita to win a penalty.
Sergio Aguero struck the from the spot - his 22nd goal of the season - and Samir Nasri and Dzeko joined him on the scoresheet inside the opening 21 minutes
A quickfire double from David Silva early in the second half put the seal on victory and City might have had three more but for three good saves from Newcastle goalkeeper Tim Krul.
One of those stops denied Wilfried Bony, City's £25million January signing, a debut goal after he appeared off the bench for the final 30 minutes.
"The goalkeeper made a great save," Bony said
"I was a little bit disappointed but when I saw the result I started to laugh
It would be great if I scored but I will take it next time."
Regardless of Bony's failure to score, it arguably appeared he had already made an impact with his presence on the bench bringing the best out of Dzeko.
The Bosnian, who was hampered by calf injuries after last scoring in September, was a handful throughout
As well as winning the penalty and scoring he set up Nasri's goal and both created chances and had some himself.
The 28-year-old said: "I am happy with the goal
It finally came back to me after those two injuries when I didn't play much, didn't score so many
Hopefully I'm back too."
While City can now look forward to Tuesday's visit of Barcelona in the Champions League in good heart, Newcastle need to pick themselves up after a demoralising afternoon.
The Magpies were comprehensively outplayed and such was the paucity of their performance that it was described as "pathetic" by their record goalscorer Alan Shearer on television.
Joe Hart did make one good save to deny Papiss Cisse, but the score was already 3-0 by then.
Newcastle remain in mid-table, 10 points above the bottom three, but manager John Carver admitted there needed to be considerable improvement before next week's home clash with struggling Aston Villa.
Carver said: "We all know this, there are three divisions within the Premier League and we know where we are.
"If you get something at a stadium like this, it is great
If not, it is not good but it is how you deal with it.
"It wasn't a good day at the office but when we get back to work on Monday we will do everything in our means to get three points against Aston Villa
That puts more pressure on us because we have to win these games in this division.
"I don't think the players gave up on the situation - I think they genuinely gave what they have - but it wasn't good enough.
"Sometimes you just have to say we were beaten by a better side with world-class players."
Source : PA
Source: PA