It was almost 2-0 just minutes later, as the West Ham defence failed to clear a cross, but were thankful to see Aguero's shot saved by Jaaskelainen.
The home side's best chance of the half followed shortly, but Ricardo Vaz Te miscued his volley.
City came close to doubling their advantage when Negredo, who had worked some space on the left hand side, drove a shot inches wide.
Diame tried his best to break through the away defence, but without a recognised striker in the West Ham starting XI, he had little support and was crowded out.
David Silva then had a rare header, but Yaya Toure came closer with a left-footed drive that Jasskelainen pushed away.