Two goals from Sergio Aguero and one from David Silva gave Pellegrini's men a 3-1 win at West Ham, who replied through Ricardo Vaz Te.
After 3-2 defeats at Cardiff and Aston Villa in their first three away games this season, City boss Pellegrini said: "Winning the game was most important for us.
"I said I think we must keep all the (good) things we have done in the other games but concentrate more on the defending. We lost two games away 3-2...to score two away is a good average.
"It's not a normal scoreline, the games we lost against Cardiff and Aston Villa - but football is like that and today we played well."
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