Sergio Aguero scored the only goal of the game in the 16th minute when clinically finishing from well inside the area after taking a nice first touch from Jesus Navas' deflected attempt.
It did not all go City's way though as the Black Cats created a number of chances only to be thwarted by visiting keeper Joe Hart who did well to deny Jermain Defoe, Billy Jones and Sunderland new boy Wahbi Khazri.
Nevertheless, the damage was done by Aguero who notched his 14th goal of the league campaign to keep City within three points of the high-flying Foxes.
For Sunderland, it was a cruel defeat which keeps them second bottom, four points adrift of safety.
- Another improved showing from the Black Cats but again they come up short. Will their influx of new players like Kirchhoff, Kone and Khazri be enough to steer them away from relegation? - Man City doing enough to stick near Leicester. Do they have the squad and know-how to overhaul the Foxes, and keep the likes of Tottenham and Arsenal at bay?
Muito bem equipa vitória dura mas nossa #CMonCity
Well done team the victory was tough but its ours #CMonCitypic.twitter.com/p04G1VnGVH
— Fernando Oficial (@Fernando_Reges) February 2, 2016
Three points that are key to staying in the race. Now it's time to rest and prepare for major upcoming matches.C'mon, City!
— Sergio Kun Aguero (@aguerosergiokun) February 2, 2016
We deserved better tonight. Thanks a lot for the support! We hope to do better the next game. #SAFC#TeamKonépic.twitter.com/q56tckBrOm
— Lamine Koné (@LamineKone_23) February 2, 2016
Sunderland's Allardyce on the disappointment of the defeat:
"It's the most disappointed I have been since I have been here with the result ending up the way it is because we deserved so much more.
"You can lose a game and say to yourself - well, some of the games we have lost since I have been here, we haven't deserved anything other than that, but today, we deserved so much more, which makes is so much more disappointing for us all."
Man City boss Pellegrini was not getting caught up in the Pep Guardiola news:
"I am just thinking about that and not the future. About the future, I really don't want to talk now. I'm just thinking about the present.
"Now we must focus our minds to beat Leicester, who are the leaders of the table, so we are just thinking about that and not about the future. We don't know what will happen to any one of us."
*Thanks to Opta
12 - Sergio Aguero has scored 12 goals in his last 10 Premier League appearances. Machine.
— OptaJoe (@OptaJoe) February 2, 2016