Eden Hazard opened the scoring for Chelsea with a penalty early in the second half here on Monday, before West Ham centre-back James Collins equalised with a neat finish in the 77th minute, reports Xinhua.
Before scoring the decisive goal, Costa could have been shown a second yellow card after catching West Ham goalkeeper with a late challenge, but the referee Anthony Taylor decided against it.
"It is important to find the right spirit and intensity. We know we can improve and we must improve a lot, but today I am pleased for my players," Conte told after the game.
Clinching first victory in the Premier League, Conte got the three points and his Chelsea is believed to be a strong competitor in the title race besides Pep Guardiola's Manchester City and Jose Mourinho's Manchester United.