Alonso put Chelsea ahead on 27 minutes with a free kick. He swept the ball over the Crystal Palace defence with his left foot.
United State men’s national team international Pulisic added Chelsea’s second 10 minutes later when Vicente Guaita saved a Mason Mount shot. The goalkeeper only managed to push the ball as far as Pulisic, though, who tapped it into the net.
Chelsea’s third came from Chalobah — who used to be a ballboy at Stamford Bridge — on 58 minutes. He struck the ball into the bottom corner from 25 yards out.
The result means Patrick Vieira starts his tenure at Crystal Palace with a loss. The ex-New York City FC boss was appointed coach after Roy Hodgson stepped down during the summer following four years in the role.