The Hammers, who hit back with a Tony Hibbert own goal, were unable to stage another comeback in front of their own fans as they remain in the relegation zone following Hull's win earlier in the day.
Everton smothered the midfield and attempted to dampen any early enthusiasm from the Hammers, who beat Aston Villa in midweek to provide a spring in their step.
Julien Faubert's crossed dangerously after one neat move from the home side and Tim Howard was brought into action when Scott Parker beat Joseph Yobo to shoot goalwards.
Yobo was more impressive soon afterwards, when snuffing out Parker's attempt to release the lively Zavon Hines.
So it was against the run of play when Saha scored after 26 minutes. Tim Cahill provided the opportunity with an inviting lay-off and the in-form French forward smacked a 20-yard finish past Rob Green.
Saha headed wide before half-time as the Toffees went in at the break a goal to the good.
With Junior Stanislas replacing Jack Collison and Luis Jimenez making way for Alessandro Diamanti, Gianfranco Zola gave his team fresh options in attack.
Stanislas shot just wide but Everton broke clear to extend their lead after 64 minutes when Gosling found himself in the clear on the right. The youngster's initial attempt was saved by Green but he greedily gobbled up the rebound.
West Ham's reply was instant as Manuel Da Costa fed Stanislas and the forward shot over Howard with Tony Hibbert smashing the ball into his own net instead of clearing the danger.
Another comeback seemed on the cards with Diamanti and Hines just off target with decent efforts and the Italian forced a save out of Howard with a free-kick.
Aside from getting the chance to boo ex-Hammer Lucas Neill when he came on as substitute, there was no late drama this time for the Upton Park faithful to enjoy as the East Londoners find themselves in the bottom three again.
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