Manager Manuel Pellegrini challenged West Ham to push for a top-six Premier League finish after they came from behind to beat Crystal Palace at London Stadium.
Second-half goals from Robert Snodgrass and Javier Hernandez and a sublime finish from Felipe Anderson gave the Hammers a third consecutive league win.
Bottom of the table after losing their first four matches of the season, West Ham moved into the top half for the first time.
"We are now in position number 10, five points from sixth position," Pellegrini said. "Maybe the first five teams have so many points that it's difficult, but we must go step by step and try to beat Fulham next week. "I always look up. I never look down. I always tell the players they must have a winning mentality. They must decide to be a big team so we must be used to seeing what is happening in front of us."