The Argentine and the Ivorian score in each half as the sombre hosts cruise to victory after losing out on the Premier League title to bitter rivals Manchester United
Sergio Aguero struck in the 28th minute to finish a sweeping City move and Yaya Toure completed a straightforward win seven minutes from time with a stunning left-footed strike into the top corner.
West Ham grabbed a goal back with their first real attempt of the match in the fourth minute added time when Andy Carroll's strike squirmed through the legs of City goalkeeper Joe Hart - but the visitors had no time left to press for an unlikely equaliser.
After bitter rivals Manchester United won the league title on Monday, the atmosphere was understandably flat at the Etihad Stadium - but City completely dominated the game against a West Ham side that offered virtually no attacking threat.
Perhaps the most significant aspect of the afternoon was the constant support from the home fans in support of under-pressure manager Roberto Mancini as the Italian faces questions following City's tame attempt to retain the title they won last year.
City made three changes to the side that lost at Tottenham last time out, with Joleon Lescott replacing Matija Nastasic at centre-back, while David Silva and Aguero returned from injury as James Milner and Edin Dzeko dropped to the bench. West Ham manager Sam Allardyce made no changes to the team that started in their win over Wigan last Saturday.
The early exchanges betrayed two sides with nothing left to play for this season with City comfortably in second place in the table and West Ham set for a mid-table finish.
In the 22nd minute, the first real chance of the game fell to Aguero after Silva’s pass deflected off Kevin Nolan. The Argentine, however, mishit his shot from 12 yards and the ball bounced back off the post.
As the clock struck 23 minutes, all sides of the ground gave a fine tribute to former City player Marc-Vivien Foe as they applauded and chanted his name to mark the 10th anniversary of his death.
It seemed to lift the atmosphere and in the 28th minute City took the lead. Samir Nasri and Silva combined with a lovely one-two in the West Ham box before the Frenchman squared for Aguero to turn the ball in from six yards.
The hosts nearly doubled their advantage immediately, but Jussi Jaaskelainen kept out Nasri’s strike before reacting quickly to deny Zabaleta as the City full-back looked to turn in the rebound.
After City lost from a winning position against Tottenham last weekend, they pushed for the cushion of a second goal after the break but were denied by some last-ditch defending from West Ham.
Aguero was denied by a brilliant block from Winston Reid, Nasri could only shoot straight at Jaaskelainen from a tight angle and then completely missed the ball after Tevez squared along the six-yard box.
In the 83rd minute, Toure made sure that there would be no way back for West Ham with a wonderful goal. The Ivorian picked the ball up on the right side of the penalty area and launched a sensational left-footed shot into the top corner.
Carroll then fired in a late consolation for the visitors in the fourth minute of added time as his right-footed shot went through Hart's legs but there was no time left for a dramatic finale.