United, who can restore their advantage to six points when they host struggling Sunderland in a later kickoff, have 39 points to City's 36.
Third-placed Chelsea, on 29, will have a game in hand due to the European champions playing the Club World Cup final in Japan on Sunday.
City, determined to come back strongly after the bitter disappointment of losing 3-2 to local rivals United in stoppage time last weekend, were a goal up after 10 minutes at St James' Park.
Ivorian midfielder Yaya Toure split the defence with a superb pass to find Samir Nasri, adjudged to be just onside, who rolled the ball back for striker Aguero to stroke home.
Nasri, mockingly described by City manager Roberto Mancini as only half a man in the defensive wall that failed to keep out Robin van Persie's winner last Sunday, did his best to make amends with a spirited but short-lived performance.
The French playmaker smacked the ball against the post in the 20th, with Tim Krul off his line and well beaten, but then limped off after 37 minutes following a heavy challenge by Davide Santon.
Javi Garcia headed City's second two minutes later, the Spaniard climbing high to meet a corner that Santon might have cleared off the line had the Italian defender not been completely wrong-footed.
City, with no room for Mario Balotelli even on the bench after Mancini said the mercurial Italian needed to train more, looked in control until Demba Ba got Newcastle back into the match with a powerful header six minutes after the break.
The goal, after Newcastle defender Fabricio Coloccini hooked the ball high into the box when a corner was cleared, was the Senegal striker's 11th in the league this season.
It spurred a Newcastle revival that could easily have seen the scores levelled.
However, a 78th minute strike from Toure to calm City's nerves with the Ivorian poking the ball through the home defence off an angled cross from Pablo Zabaleta.
Defeat for Newcastle left them in danger of tipping into the relegation places, with the club two points above the drop zone with a haul of 17 points from 17 matches, and increased the pressure on manager Alan Pardew. (Reporting by Alan Baldwin, editing by Ken Ferris)
- Sports & Recreation