After a testing week in which City's 4-2 defeat at rivals United prompted speculation about the future of manager Manuel Pellegrini and a number of leading players, victory against West Ham provided a welcome boost.
James Collins's freak own goal and Sergio Aguero's 20th league strike of the season secured a routine win and the only surprise was that City failed to add to their lead after the Argentine's 36th-minute effort.
Champions City have 64 points, one behind United who lost 1-0 at Chelsea on Saturday, and two adrift of second-placed Arsenal who have a game in hand. West Ham remain 10th having won one of their last 11 league matches.
"When we lose we have a lot of criticism and that is part of football," City midfielder Yaya Toure told Sky Sports.
"Today we showed great team spirit and it was very important to get the three points today. We will continue to fight until the end."
Newcastle United sank to a sixth straight league defeat and are not yet safe from relegation after losing 3-1 to Tottenham Hotspur at St James' Park with Harry Kane grabbing the third to reach 30 goals for the season in all competitions.
Sixth-placed Spurs are level on 57 points with fifth-placed Liverpool but have played a game more, while struggling Newcastle remain 14th with 35 points from 33 matches.
CITY BREAKTHROUGH
City's derby defeat at Old Trafford had prompted talk of the realignment of the balance of power in Manchester so the visit of a sliding West Ham side was timely.
The hosts fashioned a number of early chances with their slick passing but their breakthrough in the 18th minute came from an unlikely source.
The marauding Jesus Navas burst down the right flank and his low cross careered off defender Collins before looping over goalkeeper Adrian and deflecting in off the crossbar.
The second goal, however, was more eye-catching.
After intercepting a stray Stewart Downing pass the hosts broke with searing pace and Aguero, after exchanging passes with Navas, fired under Adrian.
City had cause for concern in the 67th minute, however, when playmaker David Silva was carried off on a stretcher after being hit in the head by Cheikhou Kouyate's elbow.
Spaniard Silva, who was treated for nearly 10 minutes on the pitch, was taken to hospital and City manager Manuel Pellegrini later said they were checking if he had broken a cheek bone.
NEWCASTLE DEMISE
There were reports of Newcastle fans boycotting the game at St James' Park because of Mike Ashley's ownership of the club and most of the 47,427 inside the stadium were unhappy to see Nacer Chadli's precise strike put Spurs ahead after 30 minutes.
Jack Colback equalised for Newcastle 18 seconds into the second half but the home side failed to stay level for long as Christian Eriksen's floated free kick into the box evaded everyone and bounced past goalkeeper Tim Krul into the net.
Harry Kane's close-range volley was then brilliantly saved by Krul but the England striker notched his 20th league goal of the season in all competitions late on when he applied a calm finish after Spurs caught Newcastle on the counter attack.
Kane, who leads the league scoring chart with Aguero, became the first Tottenham player to score 30 goals in all compeitions since ex-England striker Gary Lineker in the 1991-92 season.
