The champions had come under flak for a lacklustre start to their Premier League defence, which has been compounded by a dismal opening to their Champions League campaign.
However, Aleksandar Kolarov, Sergio Aguero and James Milner all the found the target, and even then the scoreline flattered the visitors such was City’s dominance.
And Mancini couldn’t be happier with the way his side regrouped, particularly after Wednesday’s disappointing draw with Borussia Dortmund.
“To score three goals I am happy for us,” the manager said. “It was not easy, Sunderland are a good team and it was a very difficult game. All players who played played very well.
“Victory is important before the international break and in the last two (league games) we play really well and we are improving.”
Having conceded eight goals already, City finally knuckled down in defence to record a first clean sheet of the campaign.
But centre half Joleon Lescott insisted there were still issues that needed ironing out, saying: “We are disappointed defensively this season but we are happy with the clean sheet.
“We are looking strong now and since we have come back off the international break we have been playing well.”
Sunderland manager Martin O’Neill believed his side were too sloppy with the ball in the first spell but were thoroughly outplayed in the second.
“They are a very fine side,” he said. “I thought we should have done better in the first half period. We had opportunities, but we gave ball away to easily, having said that at half-time we were still in the game but we were well beaten in the second half.”
The victory lifted City to second in the table on 15 points but still four behind leaders Chelsea, who recovered from an early scare to thump Norwich 4-1 at Stamford Bridge.
Grant Holt drilled the ball past Petr Cech after 11 minutes to give the Canaries a surprise lead. But a Blues outfit that included the controversial duo of John Terry and Ashley Cole soon went about their work, with Fernando Torres, Frank Lampard and Eden Hazard all scoring by half-time before Branislav Ivanovic powered in a fourth to wrap up the result.
Meanwhile, a late penalty from Leighton Baines helped Everton salvage a point against Wigan with a 2-2 draw at the DW Stadium.