In the latter stages, Conte sought to shut the game down, with Nemanja Matic, Willian and Kurt Zouma introduced to shore up the Blues. He has to improve.
"But for this reason we are preparing for this type of situation". So seven players. And, because they are really fit, they make that offensive transition their main offensive weapon.
In the 53rd minute, Chelsea nearly extended their lead through Marcos Alonso who skipped past two West Ham defenders but poked his shot just wide of the left-hand post.
After dominating the league leaders in the first quarter at the London Stadium, West Ham was stung by a blistering counter-attack set up by N'Golo Kante's intercept.
With the score leading 1-0 in Chelsea's favour at half time, Conte must have felt another goal was required to put the game beyond doubt and his side responded early on in the second half.
Antonio Conte: "If you ask me if my family is missing me, honestly, I have to say yes", Conte, it's not easy to stay alone, and live this experience with my family still in Italy.
"We started our season aiming to fight until the end to win the title and to be in the right position to go into next -season's Champions League". "We must work a bit on this aspect".
Super Eagles forward, Victor Moses, has been described as a complete player now after adapting to his new role as a wing back at Chelsea. Above all when you play the game after you know your opponents won the day before. They need 29 points from the Blues' remaining 12 games to be mathematically sure of lifting the trophy. "Eden and the other players did very well".
West Ham's home form has not been the best, having won just one of their last five matches across all competitions at the London Stadium, losing three and conceding 13 goals in the process.
Not surprisingly, that goal didn't go down to well with the home fans, with one charming chap squaring up to Hazard before being dragged away by a couple of stewards.
The away side were now firmly in control, dictating the tempo to a much slower, more tranquil pace; something Slaven Bilic had clearly hoped to avoid with his aggressive tactics.
"I must have confidence in my players", he said after the match.
Pedro Obiang attempted to head Hazard's corner clear but succeeded only in flicking the ball towards the Blues striker, who made no mistake.
The Hammers have been awful at home against the top six teams, and they will come into this encounter with SportyBet as underdogs with odds of (5.63).