Second-half goals from Yaya Toure and Carlos Tevez - after Joe Hart denied Frank Lampard from the penalty spot - gave City a vital victory which kept them 12 points in arrears of league leaders Manchester United.
The win was important for last season's Premier League winners and just as significant was the loss suffered by Chelsea who could drop from third if Tottenham beat West Ham United at Upton Park on Monday night.
United kept rolling along with a fourth win on the trot thanks to an absolute cracker from Rafael before Ryan Giggs added a second in the 2-0 win at QPR who stayed six points behind Reading at the foot of the table.
The Royals, who had Pavel Pogrebnyak sent off, sustained a fairly heavy defeat at the hands of Wigan Athletic who scored three goals in four minutes either side of the break with Arouna Kone on target twice.
Elsewhere, Dimitar Berbatov scored and Mark Schwarzer saved a penalty as Fulham edged Stoke City 1-0 at Craven Cottage, two late goals from Norwich City gave them a 2-1 home victory over sixth-placed Everton, Romelu Lukau's double guided West Bromwich Albion to a 2-1 triumph over Sunderland and Newcastle United rejoiced with a 4-2 win over Southampton to move to 14th.
2012/13 Barclays Premier League season scores
Newcastle United: 4 (Moussa Sissoko 33', Papiss Cisse 42', Yohan Cabaye (p) 67', Jos Hooiveld (og) 79') Southampton: 2 (Morgan Schneiderlin 3', Rickie Lambert 50') Sports Direct Arena, Newcastle-upon-Tyne - 52,259